Penalized weighted least-squares image reconstruction for positron emission tomography

Robust residual-guided iterative reconstruction for sparse-view CT in small animal imaging

Objective. We introduce a robust image reconstruction algorithm named residual-guided Golub-Kahan iterative reconstruction technique (RGIRT) designed for sparse-view computed tomography (CT), which aims at high-fidelity image reconstruction from a limited number of projection views.Approach. RGIRT utilizes an inner-outer dual iteration framework, with a flexible least square QR (FLSQR) algorithm implemented in the inner iteration and a restarted iterative scheme applied in the outer iteration. The inner FLSQR employs a flexible Golub-Kahan bidiagonalization method to reduce the size of the inverse problem, and a weighted generalized cross-validation method to adaptively estimate the regularization hyper-parameter. The inner iteration efficiently yields the intermediate reconstruction result, while the outer iteration minimizes the residual and refines the solution by using the result obtained from the inner iteration.Main results. The reconstruction performance of RGIRT is evaluated and compared to other reference methods (FBPConvNet, SART-TV, and FLSQR) using projection data from both numerical phantoms and real experimental Micro-CT data. The experimental findings, from testing various numbers of projection views and different noise levels, underscore the robustness of RGIRT. Meanwhile, theoretical analysis confirms the convergence of residual for our approach.Significance. We propose a robust iterative reconstruction algorithm for x-ray CT scans with sparse views, thereby shortening scanning time and mitigating excessive ionizing radiation exposure to small animals.

The impact of automatic tube current modulation related settings of a modern GE CT scanner on image quality and patient dose; details do matter

PURPOSE

To investigate the operation principles of the automatic tube current modulation (ATCM) of a modern GE healthcare CT scanner, and the impact of related settings on image quality and patient dose.

MATERIAL & METHODS

A dedicated phantom (Mercury 4.0) was scanned using two of the most frequently used clinical scanning protocols (chest and abdomen-pelvis). The preset protocol settings were used as starting points (reference conditions). Scan direction, scan mode (helical vs. axial), total beam width, tube potential (kVp), and ATCM settings were then modified individually to understand their impact on radiation dose and image quality. Regarding the ATCM settings, the SmartmA minimum and maximum mA limits, and the noise index (NI) values were varied. As surrogates of patient dose, the CTDIvol and DLP values of each scan were used. As surrogates of image quality were used the image noise and the detectability index (d') of five different materials (air, solid water, polystyrene, iodine, and bone) embedded in the Mercury phantom calculated with the ImQuest software.

RESULTS

The scanning direction did not have any effect on ATCM curves, unlike what has been observed in CT scanners from other manufacturers. Total beam width does matter, however, the SmartmA limit settings and kVp selection had the greatest impact on image quality and dose. It was seen that improper minimum mA limit settings practically invalidated the ATCM operation. In contrast, when full modulation was allowed without restrictions, noise standard deviation, and detectability index became much more consistent across the wide range of phantom diameters. For lower kVp settings an impressive dose reduction was observed that requires further investigation.

CONCLUSION

SmartmA is a tool that if not properly used may increase the patient doses considerably. Therefore, its settings should be carefully adjusted for each preset different clinical protocol.

Sparse-view cone-beam computed tomography iterative reconstruction based on new multi-gradient direction total variation

AIM

The accurate reconstruction of cone-beam computed tomography (CBCT) from sparse projections is one of the most important areas for study. The compressed sensing theory has been widely employed in the sparse reconstruction of CBCT. However, the total variation (TV) approach solely uses information from the i-coordinate, j-coordinate, and k-coordinate gradients to reconstruct the CBCT image.

MATERIALS AND METHODS

It is well recognized that the CBCT image can be reconstructed more accurately with more gradient information from different directions. Thus, this study introduces a novel approach, named the new multi-gradient direction total variation minimization method. The method uses gradient information from the ij-coordinate, ik-coordinate, and jk-coordinate directions to reconstruct CBCT images, which incorporates nine different types of gradient information from nine directions.

RESULTS

This study assessed the efficacy of the proposed methodology using under-sampled projections from four different experiments, including two digital phantoms, one patient's head dataset, and one physical phantom dataset. The results indicated that the proposed method achieved the lowest RMSE index and the highest SSIM index. Meanwhile, we compared the voxel intensity curves of the reconstructed images to assess the edge structure preservation. Among the various methods compared, the curves generated by the proposed method exhibited the highest level of consistency with the gold standard image curves.

CONCLUSION

In summary, the proposed method showed significant potential in enhancing the quality and accuracy of CBCT image reconstruction.

Quantum annealing-based computed tomography using variational approach for a real-number image reconstruction

Objective. Despite recent advancements in quantum computing, the limited number of available qubits has hindered progress in CT reconstruction. This study investigates the feasibility of utilizing quantum annealing-based computed tomography (QACT) with current quantum bit levels.Approach. The QACT algorithm aims to precisely solve quadratic unconstrained binary optimization problems. Furthermore, a novel approach is proposed to reconstruct images by approximating real numbers using the variational method. This approach allows for accurate CT image reconstruction using a small number of qubits. The study examines the impact of projection data quantity and noise on various image sizes ranging from 4 × 4 to 24 × 24 pixels. The reconstructed results are compared against conventional reconstruction algorithms, namely maximum likelihood expectation maximization (MLEM) and filtered back projection (FBP).Main result. By employing the variational approach and utilizing two qubits for each pixel of the image, accurate reconstruction was achieved with an adequate number of projections. Under conditions of abundant projections and lower noise levels, the image quality in QACT algorithm outperformed that of MLEM and FBP algorithms. However, in situations with limited projection data and in the presence of noise, the image quality in QACT was inferior to that in MLEM.Significance. This study developed the QACT reconstruction algorithm using the variational approach for real-number reconstruction. Remarkably, only 2 qubits were required for each pixel representation, demonstrating their sufficiency for accurate reconstruction.

CAIR: Combining integrated attention with iterative optimization learning for sparse-view CT reconstruction

Sparse-view CT is an efficient way for low dose scanning but degrades image quality. Inspired by the successful use of non-local attention in natural image denoising and compression artifact removal, we proposed a network combining integrated attention and iterative optimization learning for sparse-view CT reconstruction (CAIR). Specifically, we first unrolled the proximal gradient descent into a deep network and added an enhanced initializer between the gradient term and the approximation term. It can enhance the information flow between different layers, fully preserve the image details, and improve the network convergence speed. Secondly, the integrated attention module was introduced into the reconstruction process as a regularization term. It adaptively fuses the local and non-local features of the image which are used to reconstruct the complex texture and repetitive details of the image, respectively. Note that we innovatively designed a one-shot iteration strategy to simplify the network structure and reduce the reconstruction time while maintaining image quality. Experiments showed that the proposed method is very robust and outperforms state-of-the-art methods in terms of both quantitative and qualitative, greatly improving the preservation of structures and the removal of artifacts.

DuDoSS: Deep-learning-based dual-domain sinogram synthesis from sparsely sampled projections of cardiac SPECT

PURPOSE

Myocardial perfusion imaging (MPI) using single-photon emission-computed tomography (SPECT) is widely applied for the diagnosis of cardiovascular diseases. In clinical practice, the long scanning procedures and acquisition time might induce patient anxiety and discomfort, motion artifacts, and misalignments between SPECT and computed tomography (CT). Reducing the number of projection angles provides a solution that results in a shorter scanning time. However, fewer projection angles might cause lower reconstruction accuracy, higher noise level, and reconstruction artifacts due to reduced angular sampling. We developed a deep-learning-based approach for high-quality SPECT image reconstruction using sparsely sampled projections.

METHODS

We proposed a novel deep-learning-based dual-domain sinogram synthesis (DuDoSS) method to recover full-view projections from sparsely sampled projections of cardiac SPECT. DuDoSS utilized the SPECT images predicted in the image domain as guidance to generate synthetic full-view projections in the sinogram domain. The synthetic projections were then reconstructed into non-attenuation-corrected and attenuation-corrected (AC) SPECT images for voxel-wise and segment-wise quantitative evaluations in terms of normalized mean square error (NMSE) and absolute percent error (APE). Previous deep-learning-based approaches, including direct sinogram generation (Direct Sino2Sino) and direct image prediction (Direct Img2Img), were tested in this study for comparison. The dataset used in this study included a total of 500 anonymized clinical stress-state MPI studies acquired on a GE NM/CT 850 scanner with 60 projection angles following the injection of 99m Tc-tetrofosmin.

RESULTS

Our proposed DuDoSS generated more consistent synthetic projections and SPECT images with the ground truth than other approaches. The average voxel-wise NMSE between the synthetic projections by DuDoSS and the ground-truth full-view projections was 2.08% ± 0.81%, as compared to 2.21% ± 0.86% (p < 0.001) by Direct Sino2Sino. The averaged voxel-wise NMSE between the AC SPECT images by DuDoSS and the ground-truth AC SPECT images was 1.63% ± 0.72%, as compared to 1.84% ± 0.79% (p < 0.001) by Direct Sino2Sino and 1.90% ± 0.66% (p < 0.001) by Direct Img2Img. The averaged segment-wise APE between the AC SPECT images by DuDoSS and the ground-truth AC SPECT images was 3.87% ± 3.23%, as compared to 3.95% ± 3.21% (p = 0.023) by Direct Img2Img and 4.46% ± 3.58% (p < 0.001) by Direct Sino2Sino.

CONCLUSIONS

Our proposed DuDoSS is feasible to generate accurate synthetic full-view projections from sparsely sampled projections for cardiac SPECT. The synthetic projections and reconstructed SPECT images generated from DuDoSS are more consistent with the ground-truth full-view projections and SPECT images than other approaches. DuDoSS can potentially enable fast data acquisition of cardiac SPECT.

Extended Intraoperative Longitudinal 3-Dimensional Cone Beam Computed Tomography Imaging With a Continuous Multi-Turn Reverse Helical Scan

OBJECTIVES

Cone beam computed tomography (CBCT) imaging is becoming an indispensable intraoperative tool; however, the current field of view prevents visualization of long anatomical sites, limiting clinical utility. Here, we demonstrate the longitudinal extension of the intraoperative CBCT field of view using a multi-turn reverse helical scan and assess potential clinical utility in interventional procedures.

MATERIALS AND METHODS

A fixed-room robotic CBCT imaging system, with additional real-time control, was used to implement a multi-turn reverse helical scan. The scan consists of C-arm rotation, through a series of clockwise and anticlockwise rotations, combined with simultaneous programmed table translation. The motion properties and geometric accuracy of the multi-turn reverse helical imaging trajectory were examined using a simple geometric phantom. To assess potential clinical utility, a pedicle screw posterior fixation procedure in the thoracic spine from T1 to T12 was performed on an ovine cadaver. The multi-turn reverse helical scan was used to provide postoperative assessment of the screw insertion via cortical breach grading and mean screw angle error measurements (axial and sagittal) from 2 observers. For all screw angle measurements, the intraclass correlation coefficient was calculated to determine observer reliability.

RESULTS

The multi-turn reverse helical scans took 100 seconds to complete and increased the longitudinal coverage by 370% from 17 cm to 80 cm. Geometric accuracy was examined by comparing the measured to actual dimensions (0.2 ± 0.1 mm) and angles (0.2 ± 0.1 degrees) of a simple geometric phantom, indicating that the multi-turn reverse helical scan provided submillimeter and degree accuracy with no distortion. During the pedicle screw procedure in an ovine cadaver, the multi-turn reverse helical scan identified 4 cortical breaches, confirmed via the postoperative CT scan. Directly comparing the screw insertion angles (n = 22) measured in the postoperative multi-turn reverse helical and CT scans revealed an average difference of 3.3 ± 2.6 degrees in axial angle and 1.9 ± 1.5 degrees in the sagittal angle from 2 expert observers. The intraclass correlation coefficient was above 0.900 for all measurements (axial and sagittal) across all scan types (conventional CT, multi-turn reverse helical, and conventional CBCT), indicating excellent reliability between observers.

CONCLUSIONS

Extended longitudinal field-of-view intraoperative 3-dimensional imaging with a multi-turn reverse helical scan is feasible on a clinical robotic CBCT imaging system, enabling long anatomical sites to be visualized in a single image, including in the presence of metal hardware.

Selection criteria of image reconstruction algorithms for terahertz short-range imaging applications

Terahertz (THz) imaging has been regarded as cutting-edge technology in a wide range of applications due to its ability to penetrate through opaque materials, non-invasive nature, and its increased bandwidth capacity. Recently, THz imaging has been extensively researched in security, driver assistance technology, non-destructive testing, and medical applications. The objective of this review is to summarize the selection criteria for current state-of-the-art THz image reconstruction algorithms developed for short-range imaging applications over the last two decades. Moreover, we summarize the selected algorithms' performance and their implementation process. This study provides an in-depth understanding of the fundamentals of image reconstruction algorithms related to THz short-range imaging and future aspects of algorithm processing and selection.

CCN-CL: A content-noise complementary network with contrastive learning for low-dose computed tomography denoising

In recent years, low-dose computed tomography (LDCT) has played an increasingly important role in the diagnosis CT to reduce the potential adverse effects of x-ray radiation on patients while maintaining the same diagnostic image quality. Current deep learning-based denoising methods applied to LDCT imaging only use normal dose CT (NDCT) images as positive examples to guide the denoising process. Recent studies on contrastive learning have proved that the original images as negative examples can also be helpful for network learning. Therefore, this paper proposes a novel content-noise complementary network with contrastive learning for an LDCT denoising task. First, to better train our proposed network, a contrastive learning loss, taking the NDCT image as a positive example and the original LDCT image as a negative example to guide the network learning is added. Furthermore, we also design a network structure that combines content-noise complementary learning strategy, attention mechanism, and deformable convolution for better network performance. In an evaluation study, we compare the performance of our designed network with some of the state-of-the-art methods in the 2016 NIH-AAPM-Mayo Clinic Low Dose CT Grand Challenge dataset. The quantitative and qualitative evaluation results demonstrate the feasibility and effectiveness of applying our proposed CCN-CL network model as a new deep learning-based LDCT denoising method.

MAGIC: Manifold and Graph Integrative Convolutional Network for Low-Dose CT Reconstruction

Low-dose computed tomography (LDCT) scans, which can effectively alleviate the radiation problem, will degrade the imaging quality. In this paper, we propose a novel LDCT reconstruction network that unrolls the iterative scheme and performs in both image and manifold spaces. Because patch manifolds of medical images have low-dimensional structures, we can build graphs from the manifolds. Then, we simultaneously leverage the spatial convolution to extract the local pixel-level features from the images and incorporate the graph convolution to analyze the nonlocal topological features in manifold space. The experiments show that our proposed method outperforms both the quantitative and qualitative aspects of state-of-the-art methods. In addition, aided by a projection loss component, our proposed method also demonstrates superior performance for semi-supervised learning. The network can remove most noise while maintaining the details of only 10% (40 slices) of the training data labeled.

Unified Supervised-Unsupervised (SUPER) Learning for X-Ray CT Image Reconstruction

Traditional model-based image reconstruction (MBIR) methods combine forward and noise models with simple object priors. Recent machine learning methods for image reconstruction typically involve supervised learning or unsupervised learning, both of which have their advantages and disadvantages. In this work, we propose a unified supervised-unsupervised (SUPER) learning framework for X-ray computed tomography (CT) image reconstruction. The proposed learning formulation combines both unsupervised learning-based priors (or even simple analytical priors) together with (supervised) deep network-based priors in a unified MBIR framework based on a fixed point iteration analysis. The proposed training algorithm is also an approximate scheme for a bilevel supervised training optimization problem, wherein the network-based regularizer in the lower-level MBIR problem is optimized using an upper-level reconstruction loss. The training problem is optimized by alternating between updating the network weights and iteratively updating the reconstructions based on those weights. We demonstrate the learned SUPER models' efficacy for low-dose CT image reconstruction, for which we use the NIH AAPM Mayo Clinic Low Dose CT Grand Challenge dataset for training and testing. In our experiments, we studied different combinations of supervised deep network priors and unsupervised learning-based or analytical priors. Both numerical and visual results show the superiority of the proposed unified SUPER methods over standalone supervised learning-based methods, iterative MBIR methods, and variations of SUPER obtained via ablation studies. We also show that the proposed algorithm converges rapidly in practice.

A Novel Iterative MLEM Image Reconstruction Algorithm Based on Beltrami Filter: Application to ECT Images

The implementation of emission-computed tomography (ECT), including positron emission tomography and single-photon emission-computed tomography, has been an important research topic in recent years and is of significant and practical importance. However, the slow rate of convergence and the computational complexity have severely impeded the efficient implementation of iterative reconstruction. By combining the maximum-likelihood expectation maximization (MLEM) iteratively along with the Beltrami filter, this paper proposes a new approach to reformulate the MLEM algorithm. Beltrami filtering is applied to an image obtained using the MLEM algorithm for each iteration. The role of Beltrami filtering is to remove mainly out-of-focus slice blurs, which are artifacts present in most existing images. To improve the quality of an image reconstructed using MLEM, the Beltrami filter employs similar structures, which in turn reduce the number of errors in the reconstructed image. Numerical image reconstruction tomography experiments have demonstrated the performance capability of the proposed algorithm in terms of an increase in signal-to-noise ratio (SNR) and the recovery of fine details that can be hidden in the data. The SNR and visual inspections of the reconstructed images are significantly improved compared to those of a standard MLEM. We conclude that the proposed algorithm provides an edge-preserving image reconstruction and substantially suppress noise and edge artifacts.

Photoacoustic computed tomography for functional human brain imaging [Invited]

The successes of magnetic resonance imaging and modern optical imaging of human brain function have stimulated the development of complementary modalities that offer molecular specificity, fine spatiotemporal resolution, and sufficient penetration simultaneously. By virtue of its rich optical contrast, acoustic resolution, and imaging depth far beyond the optical transport mean free path (∼1 mm in biological tissues), photoacoustic computed tomography (PACT) offers a promising complementary modality. In this article, PACT for functional human brain imaging is reviewed in its hardware, reconstruction algorithms, in vivo demonstration, and potential roadmap.

Physics-based iterative reconstruction for dual-source and flying focal spot computed tomography

PURPOSE

For single-source helical Computed Tomography (CT), both Filtered-Back Projection (FBP) and statistical iterative reconstruction have been investigated. However, for dual-source CT with flying focal spot (DS-FFS CT), a statistical iterative reconstruction that accurately models the scanner geometry and acquisition physics remains unknown to researchers. Therefore, our purpose is to present a novel physics-based iterative reconstruction method for DS-FFS CT and assess its image quality.

METHODS

Our algorithm uses precise physics models to reconstruct from the native cone-beam geometry and interleaved dual-source helical trajectory of a DS-FFS CT. To do so, we construct a noise physics model to represent data acquisition noise and a prior image model to represent image noise and texture. In addition, we design forward system models to compute the locations of deflected focal spots, the dimension, and sensitivity of voxels and detector units, as well as the length of intersection between x-rays and voxels. The forward system models further represent the coordinated movement between the dual sources by computing their x-ray coverage gaps and overlaps at an arbitrary helical pitch. With the above models, we reconstruct images by an advanced Consensus Equilibrium (CE) numerical method to compute the maximum a posteriori estimate to a joint optimization problem that simultaneously fits all models.

RESULTS

We compared our reconstruction with Siemens ADMIRE, which is the clinical standard hybrid iterative reconstruction (IR) method for DS-FFS CT, in terms of spatial resolution, noise profile, and image artifacts through both phantoms and clinical scan datasets. Experiments show that our reconstruction has a higher spatial resolution, with a Task-Based Modulation Transfer Function (MTF_task ) consistently higher than the clinical standard hybrid IR. In addition, our reconstruction shows a reduced magnitude of image undersampling artifacts than the clinical standard.

CONCLUSIONS

By modeling a precise geometry and avoiding data rebinning or interpolation, our physics-based reconstruction achieves a higher spatial resolution and fewer image artifacts with smaller magnitude than the clinical standard hybrid IR.

SPECTnet: a deep learning neural network for SPECT image reconstruction

Background

Single photon emission computed tomography (SPECT) is an important functional tool for clinical diagnosis and scientific research of brain disorders, but suffers from limited spatial resolution and high noise due to hardware design and imaging physics. The present study is to develop a deep learning technique for SPECT image reconstruction that directly converts raw projection data to image with high resolution and low noise, while an efficient training method specifically applicable to medical image reconstruction is presented.

Methods

A custom software was developed to generate 20,000 2-D brain phantoms, of which 16,000 were used to train the neural network, 2,000 for validation, and the final 2,000 for testing. To reduce development difficulty, a two-step training strategy for network design was adopted. We first compressed full-size activity image (128×128 pixels) to a one-D vector consisting of 256×1 pixels, accomplished by an autoencoder (AE) consisting of an encoder and a decoder. The vector is a good representation of the full-size image in a lower-dimensional space and was used as a compact label to develop the second network that maps between the projection-data domain and the vector domain. Since the label had 256 pixels only, the second network was compact and easy to converge. The second network, when successfully developed, was connected to the decoder (a portion of AE) to decompress the vector to a regular 128×128 image. Therefore, a complex network was essentially divided into two compact neural networks trained separately in sequence but eventually connectable.

Results

A total of 2,000 test examples, a synthetic brain phantom, and de-identified patient data were used to validate SPECTnet. Results obtained from SPECTnet were compared with those obtained from our clinic OS-EM method. Images with lower noise and more accurate information in the uptake areas were obtained by SPECTnet.

Conclusions

The challenge of developing a complex deep neural network is reduced by training two separate compact connectable networks. The combination of the two networks forms the full version of SPECTnet. Results show that the developed neural network can produce more accurate SPECT images.

OMEGA-open-source emission tomography software

In this paper we present OMEGA, an open-source software, for efficient and fast image reconstruction in positron emission tomography (PET). OMEGA uses the scripting language of MATLAB and GNU Octave allowing reconstruction of PET data with a MATLAB or GNU Octave interface. The goal of OMEGA is to allow easy and fast reconstruction of any PET data, and to provide a computationally efficient, easy-access platform for development of new PET algorithms with built-in forward and backward projection operations available to the user as a MATLAB/Octave class. OMEGA also includes direct support for GATE simulated data, facilitating easy evaluation of the new algorithms using Monte Carlo simulated PET data. OMEGA supports parallel computing by utilizing OpenMP for CPU implementations and OpenCL for GPU allowing any hardware to be used. OMEGA includes built-in function for the computation of normalization correction and allows several other corrections to be applied such as attenuation, randoms or scatter. OMEGA includes several different maximum-likelihood and maximum a posteriori (MAP) algorithms with several different priors. The user can also input their own priors to the built-in MAP functions. The image reconstruction in OMEGA can be computed either by using an explicitly computed system matrix or with a matrix-free formalism, where the latter can be accelerated with OpenCL. We provide an overview on the software and present some examples utilizing the different features of the software.

An improved patch-based regularization method for PET image reconstruction

Background

Statistical reconstruction methods based on penalized maximum likelihood (PML) are being increasingly used in positron emission tomography (PET) imaging to reduce noise and improve image quality. Wang and Qi proposed a patch-based edge-preserving penalties algorithm that can be implemented in three simple steps: a maximum-likelihood expectation-maximization (MLEM) image update, an image smoothing step, and a pixel-by-pixel image fusion step. The pixel-by-pixel image fusion step, which fuses the MLEM updated image and the smoothed image, involves a trade-off between preserving the fine structural features of an image and suppressing noise. Particularly when reconstructing images from low-count data, this step cannot preserve fine structural features in detail. To better preserve these features and accelerate the algorithm convergence, we proposed to improve the patch-based regularization reconstruction method.

Methods

Our improved method involved adding a total variation (TV) regularization step following the MLEM image update in the patch-based algorithm. A feature refinement (FR) step was then used to extract the lost fine structural features from the residual image between the TV regularized image and the fused image based on patch regularization. These structural features would then be added back to the fused image. With the addition of these steps, each iteration of the image should gain more structural information. A brain phantom simulation experiment and a mouse study were conducted to evaluate our proposed improved method. Brain phantom simulation with added noise were used to determine the feasibility of the proposed algorithm and its acceleration of convergence. Data obtained from the mouse study were divided into event count sets to validate the performance of the proposed algorithm when reconstructing images from low-count data. Five criteria were used for quantitative evaluation: signal-to-noise ratio (SNR), covariance (COV), contrast recovery coefficient (CRC), regional relative bias, and relative variance.

Results

The bias and variance of the phantom brain image reconstructed using the patch-based method were 0.421 and 5.035, respectively, and this process took 83.637 seconds. The bias and variance of the image reconstructed by the proposed improved method, however, were 0.396 and 4.568, respectively, and this process took 41.851 seconds. This demonstrates that the proposed algorithm accelerated the reconstruction convergence. The CRC of the phantom brain image reconstructed using the patch-based method was iterated 20 times and reached 0.284, compared with the proposed method, which reached 0.446. When using a count of 5,000 K data obtained from the mouse study, both the patch-based method and the proposed method reconstructed images similar to the ground truth image. The intensity of the ground truth image was 88.3, and it was located in the 102^nd row and the 116^th column. However, when the count was reduced to below 40 K, and the patch-based method was used, image quality was significantly reduced. This effect was not observed when the proposed method was used. When a count of 40 K was used, the image intensity was 58.79 when iterated 100 times by the patch-based method, and it was located in the 102^nd row and the 116^th column, while the intensity when iterated 50 times by the proposed method was 63.83. This suggests that the proposed method improves image reconstruction from low-count data.

Conclusions

This improved method of PET image reconstruction could potentially improve the quality of PET images faster than other methods and also produce better reconstructions from low-count data.

FBP-Net for direct reconstruction of dynamic PET images

Dynamic positron emission tomography (PET) imaging can provide information about metabolic changes over time, used for kinetic analysis and auxiliary diagnosis. Existing deep learning-based reconstruction methods have too many trainable parameters and poor generalization, and require mass data to train the neural network. However, obtaining large amounts of medical data is expensive and time-consuming. To reduce the need for data and improve the generalization of network, we combined the filtered back-projection (FBP) algorithm with neural network, and proposed FBP-Net which could directly reconstruct PET images from sinograms instead of post-processing the rough reconstruction images obtained by traditional methods. The FBP-Net contained two parts: the FBP part and the denoiser part. The FBP part adaptively learned the frequency filter to realize the transformation from the detector domain to the image domain, and normalized the coarse reconstruction images obtained. The denoiser part merged the information of all time frames to improve the quality of dynamic PET reconstruction images, especially the early time frames. The proposed FBP-Net was performed on simulation and real dataset, and the results were compared with the state-of-art U-net and DeepPET. The results showed that FBP-Net did not tend to overfit the training set and had a stronger generalization.

C-arm orbits for metal artifact avoidance (MAA) in cone-beam CT

Metal artifacts present a challenge to cone-beam CT (CBCT) image-guided surgery, obscuring visualization of metal instruments and adjacent anatomy-often in the very region of interest pertinent to the imaging/surgical tasks. We present a method to reduce the influence of metal artifacts by prospectively defining an image acquisition protocol-viz., the C-arm source-detector orbit-that mitigates metal-induced biases in the projection data. The metal artifact avoidance (MAA) method is compatible with simple mobile C-arms, does not require exact prior information on the patient or metal implants, and is consistent with 3D filtered backprojection (FBP), more advanced (e.g. polyenergetic) model-based image reconstruction (MBIR), and metal artifact reduction (MAR) post-processing methods. The MAA method consists of: (i) coarse localization of metal objects in the field-of-view (FOV) via two or more low-dose scout projection views and segmentation (e.g. a simple U-Net) in coarse backprojection; (ii) model-based prediction of metal-induced x-ray spectral shift for all source-detector vertices accessible by the imaging system (e.g. gantry rotation and tilt angles); and (iii) identification of a circular or non-circular orbit that reduces the variation in spectral shift. The method was developed, tested, and evaluated in a series of studies presenting increasing levels of complexity and realism, including digital simulations, phantom experiment, and cadaver experiment in the context of image-guided spine surgery (pedicle screw implants). The MAA method accurately predicted tilted circular and non-circular orbits that reduced the magnitude of metal artifacts in CBCT reconstructions. Realistic distributions of metal instrumentation were successfully localized (0.71 median Dice coefficient) from 2-6 low-dose scout views even in complex anatomical scenes. The MAA-predicted tilted circular orbits reduced root-mean-square error (RMSE) in 3D image reconstructions by 46%-70% and 'blooming' artifacts (apparent width of the screw shaft) by 20-45%. Non-circular orbits defined by MAA achieved a further ∼46% reduction in RMSE compared to the best (tilted) circular orbit. The MAA method presents a practical means to predict C-arm orbits that minimize spectral bias from metal instrumentation. Resulting orbits-either simple tilted circular orbits or more complex non-circular orbits that can be executed with a motorized multi-axis C-arm-exhibited substantial reduction of metal artifacts in raw CBCT reconstructions by virtue of higher fidelity projection data, which are in turn compatible with subsequent MAR post-processing and/or polyenergetic MBIR to further reduce artifacts.

Characterization of tissue-specific pre-log Bayesian CT reconstruction by texture-dose relationship

PURPOSE

Tissue textures have been recognized as biomarkers for various clinical tasks. In computed tomography (CT) image reconstruction, it is important but challenging to preserve the texture when lowering x-ray exposure from full- toward low-/ultra-low dose level. Therefore, this paper aims to explore the texture-dose relationship within one tissue-specific pre-log Bayesian CT reconstruction algorithm.

METHODS

To enhance the texture in ultra-low dose CT (ULdCT) reconstruction, this paper presents a Bayesian type algorithm. A shifted Poisson model is adapted to describe the statistical properties of pre-log data, and a tissue-specific Markov random field prior (MRFt) is used to incorporate tissue texture from previous full-dose CT, thus called SP-MRFt algorithm. Utilizing the SP-MRFt algorithm, we investigated tissue texture degradation as a function of x-ray dose levels from full dose (100 mAs/120 kVp) to ultralow dose (1 mAs/120 kVp) by using quantitative texture-based evaluation metrics.

RESULTS

Experimental results show the SP-MRFt algorithm outperforms conventional filtered back projection (FBP) and post-log domain penalized weighted least square MRFt (PWLS-MRFt) in terms of noise suppression and texture preservation. Comparable results are also obtained with shifted Poisson model with 7 × 7 Huber MRF weights (SP-Huber7). The investigation on texture-dose relationship shows that the quantified texture measures drop monotonically as dose level decreases, and interestingly a turning point is observed on the texture-dose response curve.

CONCLUSIONS

This important observation implies that there exists a minimum dose level, at which a given CT scanner (hardware configuration and image reconstruction software) can achieve without compromising clinical tasks. Moreover, the experiment results show that the variance of electronic noise has higher impact than the mean to the texture-dose relationship.

Generative adversarial network based regularized image reconstruction for PET

Positron emission tomography (PET) is an ill-posed inverse problem and suffers high noise due to limited number of detected events. Prior information can be used to improve the quality of reconstructed PET images. Deep neural networks have also been applied to regularized image reconstruction. One method is to use a pretrained denoising neural network to represent the PET image and to perform a constrained maximum likelihood estimation. In this work, we propose to use a generative adversarial network (GAN) to further improve the network performance. We also modify the objective function to include a data-matching term on the network input. Experimental studies using computer-based Monte Carlo simulations and real patient datasets demonstrate that the proposed method leads to noticeable improvements over the kernel-based and U-net-based regularization methods in terms of lesion contrast recovery versus background noise trade-offs.

A Learned Reconstruction Network for SPECT Imaging

A neural network designed specifically for SPECT image reconstruction was developed. The network reconstructed activity images from SPECT projection data directly. Training was performed through a corpus of training data including that derived from digital phantoms generated from custom software and the corresponding projection data obtained from simulation. When using the network to reconstruct images, input projection data were initially fed to two fully connected (FC) layers to perform a basic reconstruction. Then the output of the FC layers and an attenuation map were delivered to five convolutional layers for signal-decay compensation and image optimization. To validate the system, data not used in training, simulated data from the Zubal human brain phantom, and clinical patient data were used to test reconstruction performance. Reconstructed images from the developed network proved closer to the truth with higher resolution and quantitative accuracy than those from conventional OS-EM reconstruction. To understand better the operation of the network for reconstruction, intermediate results from hidden layers were investigated for each step of the processing. The network system was also retrained with noisy projection data and compared with that developed with noise-free data. The retrained network proved even more robust after having learned to filter noise. Finally, we showed that the network still provided sharp images when using reduced view projection data (retrained with reduced view data).

Constructing a tissue-specific texture prior by machine learning from previous full-dose scan for Bayesian reconstruction of current ultralow-dose CT images

Purpose: Bayesian theory provides a sound framework for ultralow-dose computed tomography (ULdCT) image reconstruction with two terms for modeling the data statistical property and incorporating a priori knowledge for the image that is to be reconstructed. We investigate the feasibility of using a machine learning (ML) strategy, particularly the convolutional neural network (CNN), to construct a tissue-specific texture prior from previous full-dose computed tomography. Approach: Our study constructs four tissue-specific texture priors, corresponding with lung, bone, fat, and muscle, and integrates the prior with the prelog shift Poisson (SP) data property for Bayesian reconstruction of ULdCT images. The Bayesian reconstruction was implemented by an algorithm called SP-CNN-T and compared with our previous Markov random field (MRF)-based tissue-specific texture prior algorithm called SP-MRF-T. Results: In addition to conventional quantitative measures, mean squared error and peak signal-to-noise ratio, structure similarity index, feature similarity, and texture Haralick features were used to measure the performance difference between SP-CNN-T and SP-MRF-T algorithms in terms of the structure and tissue texture preservation, demonstrating the feasibility and the potential of the investigated ML approach. Conclusions: Both training performance and image reconstruction results showed the feasibility of constructing CNN texture prior model and the potential of improving the structure preservation of the nodule comparing to our previous regional tissue-specific MRF texture prior model.

Maximum likelihood reconstruction for grating-based X-ray microscopy

The combination of grating-based phase-contrast imaging with X-ray microscopy can result in a complicated image formation. Generally, transverse shifts of the interference fringes are nonlinearly dependent on phase differences of the measured wave front. We present an iterative reconstruction scheme based on a regularized maximum likelihood cost function that fully takes this dependency into account. The scheme is validated by numerical simulations. It is particularly advantageous at low photon numbers and when the premises for deconvolution-based reconstructions are not met. Our reconstruction scheme hence enables a broader applicability of X-ray grating interferometry in imaging and wave front sensing.

From Fienup's phase retrieval techniques to regularized inversion for in-line holography: tutorial

This paper includes a tutorial on how to reconstruct in-line holograms using an inverse problems approach, starting with modeling the observations, selecting regularizations and constraints, and ending with the design of a reconstruction algorithm. A special focus is placed on the connections between the numerous alternating projections strategies derived from Fienup's phase retrieval technique and the inverse problems framework. In particular, an interpretation of Fienup's algorithm as iterates of a proximal gradient descent for a particular cost function is given. Reconstructions from simulated and experimental holograms of micrometric beads illustrate the theoretical developments. The results show that the transition from alternating projections techniques to the inverse problems formulation is straightforward and advantageous.

3D Tensor Based Nonlocal Low Rank Approximation in Dynamic PET Reconstruction

Reconstructing images from multi-view projections is a crucial task both in the computer vision community and in the medical imaging community, and dynamic positron emission tomography (PET) is no exception. Unfortunately, image quality is inevitably degraded by the limitations of photon emissions and the trade-off between temporal and spatial resolution. In this paper, we develop a novel tensor based nonlocal low-rank framework for dynamic PET reconstruction. Spatial structures are effectively enhanced not only by nonlocal and sparse features, but momentarily by tensor-formed low-rank approximations in the temporal realm. Moreover, the total variation is well regularized as a complementation for denoising. These regularizations are efficiently combined into a Poisson PET model and jointly solved by distributed optimization. The experiments demonstrated in this paper validate the excellent performance of the proposed method in dynamic PET.

Convolutional Sparse Coding for Compressed Sensing CT Reconstruction

Over the past few years, dictionary learning (DL)-based methods have been successfully used in various image reconstruction problems. However, the traditional DL-based computed tomography (CT) reconstruction methods are patch-based and ignore the consistency of pixels in overlapped patches. In addition, the features learned by these methods always contain shifted versions of the same features. In recent years, convolutional sparse coding (CSC) has been developed to address these problems. In this paper, inspired by several successful applications of CSC in the field of signal processing, we explore the potential of CSC in sparse-view CT reconstruction. By directly working on the whole image, without the necessity of dividing the image into overlapped patches in DL-based methods, the proposed methods can maintain more details and avoid artifacts caused by patch aggregation. With predetermined filters, an alternating scheme is developed to optimize the objective function. Extensive experiments with simulated and real CT data were performed to validate the effectiveness of the proposed methods. The qualitative and quantitative results demonstrate that the proposed methods achieve better performance than the several existing state-of-the-art methods.

Negative binomial maximum likelihood expectation maximization (NB-MLEM) algorithm for reconstruction of pre-corrected PET data

PURPOSE

Positron emission tomography (PET) image reconstruction is usually performed using maximum likelihood (ML) iterative reconstruction methods, under the assumption of Poisson distributed data. Pre-correcting raw measured counts, this assumption is no longer realistic. The goal of this work is to develop a reconstruction algorithm based on the Negative Binomial (NB) distribution, which can generalize over the Poisson distribution in case of over-dispersion of raw data, that may occur if sinogram pre-correction is used.

METHODS

The mathematical derivation of a Negative Binomial Maximum Likelihood Expectation-Maximization (NB-MLEM) algorithm is presented. A simulation study to compare the performance of the proposed NB-MLEM algorithm with respect to a Poisson-based MLEM (P-MLEM) method was performed, in reconstructing PET data. The proposed NB-MLEM reconstruction was tested on a real phantom and human brain data.

RESULTS

For the property of NB distribution, it is a generalization of the conventional P-MLEM: for not over dispersed data, the proposed NB-MLEM algorithm behaves like the conventional P-MLEM; for over-dispersed PET data, the additional evaluation of the dispersion parameter after each reconstruction iteration leads to a more accurate final image with respect to P-MLEM.

CONCLUSIONS

A novel approach for PET image reconstruction from pre-corrected data has been developed, which exhibits a statistical behavior that deviates from the Poisson distribution. Simulation study and preliminary tests on real data showed how the NB-MLEM algorithm, being able to explain the over-dispersion of pre-corrected data, can outperform other algorithms that assume no over-dispersion of pre-corrected data, while still not accounting for the presence of negative data, such as P-MLEM.

Factor Analysis of Dynamic PET Images: Beyond Gaussian Noise

Factor analysis has proven to be a relevant tool for extracting tissue time-activity curves (TACs) in dynamic PET images, since it allows for an unsupervised analysis of the data. Reliable and interpretable results are possible only if it is considered with respect to suitable noise statistics. However, the noise in reconstructed dynamic PET images is very difficult to characterize, despite the Poissonian nature of the count rates. Rather than explicitly modeling the noise distribution, this paper proposes to study the relevance of several divergence measures to be used within a factor analysis framework. To this end, the β -divergence, widely used in other applicative domains, is considered to design the data-fitting term involved in three different factor models. The performances of the resulting algorithms are evaluated for different values of β , in a range covering Gaussian, Poissonian, and Gamma-distributed noises. The results obtained on two different types of synthetic images and one real image show the interest of applying non-standard values of β to improve the factor analysis.

A Feasibility Study of Extracting Tissue Textures From a Previous Full-Dose CT Database as Prior Knowledge for Bayesian Reconstruction of Current Low-Dose CT Images

Markov random field (MRF) has been widely used to incorporate a priori knowledge as penalty or regularizer to preserve edge sharpness while smoothing the region enclosed by the edge for pieces-wise smooth image reconstruction. In our earlier study, we proposed a type of MRF reconstruction method for low-dose CT (LdCT) scans using tissue-specific textures extracted from the same patient's previous full-dose CT (FdCT) scans as prior knowledge. It showed advantages in clinical applications. This paper aims to remove the constraint of using previous data of the same patient. We investigated the feasibility of extracting the tissue-specific MRF textures from an FdCT database to reconstruct a LdCT image of another patient. This feasibility study was carried out by experiments designed as follows. We constructed a tissue-specific MRF-texture database from 3990 FdCT scan slices of 133 patients who were scheduled for lung nodule biopsy. Each patient had one FdCT scan (120 kVp/100 mAs) and one LdCT scan (120 kVp/20 mAs) prior to biopsy procedure. When reconstructing the LdCT image of one patient among the 133 patients, we ranked the closeness of the MRF-textures from the other 132 patients saved in the database and used them as the a prior knowledge. Then, we evaluated the reconstructed image quality using Haralick texture measures. For any patient within our database, we found more than eighteen patients' FdCT MRF texures can be used without noticeably changing the Haralick texture measures on the lung nodules (to be biopsied). These experimental outcomes indicate it is promising that a sizable FdCT texture database could be used to enhance Bayesian reconstructions of any incoming LdCT scans.

A survey of computational frameworks for solving the acoustic inverse problem in three-dimensional photoacoustic computed tomography

Photoacoustic computed tomography (PACT), also known as optoacoustic tomography, is an emerging imaging technique that holds great promise for biomedical imaging. PACT is a hybrid imaging method that can exploit the strong endogenous contrast of optical methods along with the high spatial resolution of ultrasound methods. In its canonical form that is addressed in this article, PACT seeks to estimate the photoacoustically-induced initial pressure distribution within the object. Image reconstruction methods are employed to solve the acoustic inverse problem associated with the image formation process. When an idealized imaging scenario is considered, analytic solutions to the PACT inverse problem are available; however, in practice, numerous challenges exist that are more readily addressed within an optimization-based, or iterative, image reconstruction framework. In this article, the PACT image reconstruction problem is reviewed within the context of modern optimization-based image reconstruction methodologies. Imaging models that relate the measured photoacoustic wavefields to the sought-after object function are described in their continuous and discrete forms. The basic principles of optimization-based image reconstruction from discrete PACT measurement data are presented, which includes a review of methods for modeling the PACT measurement system response and other important physical factors. Non-conventional formulations of the PACT image reconstruction problem, in which acoustic parameters of the medium are concurrently estimated along with the PACT image, are also introduced and reviewed.

Confidence Interval Constraint-Based Regularization Framework for PET Quantization

In this paper, a new generic regularized reconstruction framework based on confidence interval constraints for tomographic reconstruction is presented. As opposed to usual state-of-the-art regularization methods that try to minimize a cost function expressed as the sum of a data-fitting term and a regularization term weighted by a scalar parameter, the proposed algorithm is a two-step process. The first step concentrates on finding a set of images that rely on the direct estimation of confidence intervals for each reconstructed value. Then, the second step uses confidence intervals as a constraint to choose the most appropriate candidate according to a regularization criterion. Two different constraints are proposed in this paper. The first one has the main advantage of strictly ensuring that the regularized solution will respect the interval-valued data-fitting constraint, thus preventing over-smoothing of the solution while offering interesting properties in terms of spatial and statistical bias/variance trade-off. Another regularization proposition based on the design of a smoother constraint also with appealing properties is proposed as an alternative. The competitiveness of the proposed framework is illustrated in comparison to other regularization schemes using analytical and GATE-based simulation and real PET acquisition.

DeepPET: A deep encoder-decoder network for directly solving the PET image reconstruction inverse problem

The purpose of this research was to implement a deep learning network to overcome two of the major bottlenecks in improved image reconstruction for clinical positron emission tomography (PET). These are the lack of an automated means for the optimization of advanced image reconstruction algorithms, and the computational expense associated with these state-of-the art methods. We thus present a novel end-to-end PET image reconstruction technique, called DeepPET, based on a deep convolutional encoder-decoder network, which takes PET sinogram data as input and directly and quickly outputs high quality, quantitative PET images. Using simulated data derived from a whole-body digital phantom, we randomly sampled the configurable parameters to generate realistic images, which were each augmented to a total of more than 291,000 reference images. Realistic PET acquisitions of these images were simulated, resulting in noisy sinogram data, used for training, validation, and testing the DeepPET network. We demonstrated that DeepPET generates higher quality images compared to conventional techniques, in terms of relative root mean squared error (11%/53% lower than ordered subset expectation maximization (OSEM)/filtered back-projection (FBP), structural similarity index (1%/11% higher than OSEM/FBP), and peak signal-to-noise ratio (1.1/3.8 dB higher than OSEM/FBP). In addition, we show that DeepPET reconstructs images 108 and 3 times faster than OSEM and FBP, respectively. Finally, DeepPET was successfully applied to real clinical data. This study shows that an end-to-end encoder-decoder network can produce high quality PET images at a fraction of the time compared to conventional methods.

Multi-energy computed tomography reconstruction using a nonlocal spectral similarity model

Multi-energy computed tomography (MECT) is able to acquire simultaneous multi-energy measurements from one scan. In addition, it allows material differentiation and quantification effectively. However, due to the limited energy bin width, the number of photons detected in an energy-specific channel is smaller than that in traditional CT, which results in image quality degradation. To address this issue, in this work, we develop a statistical iterative reconstruction algorithm to acquire high-quality MECT images and high-accuracy material-specific images. Specifically, this algorithm fully incorporates redundant self-similarities within nonlocal regions in the MECT image at one bin and rich spectral similarities among MECT images at all bins. For simplicity, the presented algorithm is referred to as 'MECT-NSS'. Moreover, an efficient optimization algorithm is developed to solve the MECT-NSS objective function. Then, a comprehensive evaluation of parameter selection for the MECT-NSS algorithm is conducted. In the experiment, the datasets include images from three phantoms and one patient to validate and evaluate the MECT-NSS reconstruction performance. The qualitative and quantitative results demonstrate that the presented MECT-NSS can successfully yield better MECT image quality and more accurate material estimation than the competing algorithms.

Imaging of fiber-like structures in digital breast tomosynthesis

Fiber-like features are an important aspect of breast imaging. Vessels and ducts are present in all breast images, and spiculations radiating from a mass can indicate malignancy. Accordingly, fiber objects are one of the three types of signals used in the American College of Radiology digital mammography (ACR-DM) accreditation phantom. Our work focuses on the image properties of fiber-like structures in digital breast tomosynthesis (DBT) and how image reconstruction can affect their appearance. The impact of DBT image reconstruction algorithm and regularization strength on the conspicuity of fiber-like signals of various orientations is investigated in simulation. A metric is developed to characterize this orientation dependence and allow for quantitative comparison of algorithms and associated parameters in the context of imaging fiber signals. The imaging properties of fibers, characterized in simulation, are then demonstrated in detail with physical DBT data of the ACR-DM phantom. The characterization of imaging of fiber signals is used to explain features of an actual clinical DBT case. For the algorithms investigated, at low regularization setting, the results show a striking variation in conspicuity as a function of orientation in the viewing plane. In particular, the conspicuity of fibers nearly aligned with the plane of the x-ray source trajectory is decreased relative to more obliquely oriented fibers. Increasing regularization strength mitigates this orientation dependence at the cost of increasing depth blur of these structures.

Positron emission tomography image reconstruction using feature extraction

PURPOSE

To reduce the cost of positron emission tomography (PET) scanning systems, image reconstruction algorithms for low-sampled data have been extensively studied. However, the current method based on total variation (TV) minimization regularization nested in the maximum likelihood-expectation maximization (MLEM) algorithm cannot distinguish true structures from noise resulting losing some fine features in the images. Thus, this work aims to recover fine features lost in the MLEM-TV algorithm from low-sampled data.

METHOD

A feature refinement (FR) approach previously developed for statistical interior computed tomography (CT) reconstruction is applied to PET imaging to recover fine features in this study. The proposed method starts with a constant initial image and the FR step is performed after each MLEM-TV iteration to extract the desired structural information lost during TV minimization. A feature descriptor is specifically designed to distinguish structure from noise and artifacts. A modified steepest descent method is adopted to minimize the objective function. After evaluating the impacts of different patch sizes on the outcome of the presented method, an optimal patch size of 7×7 is selected in this study to balance structure-detection ability and computational efficiency.

RESULTS

Applying MLEM-TV-FR algorithm to the simulated brain PET imaging using an emission activity phantom, a standard Shepp-Logan phantom, and mouse results in the increased peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) as comparing to using the conventional MLEM-TV algorithm, as well as the substantial reduction of the used sampling numbers, which improves the computational efficiency.

CONCLUSIONS

The presented algorithm can achieve image quality superior to that of the MLEM and MLEM-TV approaches in terms of the preservation of fine structure and the suppression of undesired artifacts and noise, indicating its useful potential for low-sampled data in PET imaging.

Structure tensor total variation for CBCT reconstruction

The total variation (TV) regularization has been widely used in statistically iterative cone-beam computed tomography (CBCT) reconstruction, showing ability to preserve object edges. However, the TV regularization can also produce staircase effect and tend to over-smooth the reconstructed images due to its piecewise constant assumption. In this study, we proposed to use the structure tensor total variation (STV) that penalizes the eigenvalues of the structure tensor for CBCT reconstruction. The STV penalty extends the TV penalty, with many important properties maintained such as convexity and rotation and translation invariance. The STV penalty utilizes gradient information more effectively and has a stronger ability to capture local image structural variation. The objective function was constructed with the penalized weighted least-square (PWLS) strategy and the gradient descent (GD) method was used to optimize the objective function. Besides, we investigated whether the norms involved in the STV penalty affected the reconstruction performance and found that the l1-norm gave the better performance than the l2-norm and l ∞-norm. We also examined performance of the STV penalties constructed using different kernel functions and found that the STV with the Gaussian kernel had the best performance, and the STVs with Uniform, Logistic, and Sigmoid kernels had similar performance to each other. We evaluated our reconstruction method with the STV penalty on computer simulated phantoms and physical phantoms. The results demonstrated that STV led to better reconstruction performance than TV, both visually and quantitatively. For the Catphan 600 physical phantom, the STV1 penalty was 175% and 623% better than the low-dose FDK and the high-dose FDK, and 14% better than the TV penalty at the matched noise level, according to the average contrast-to-noise ratio (CNR); while for the Compressed Sensing simulation phantom, the peak signal to noise ratio (PSNR) of reconstructed results using STV1, STV2, and STV ∞ were 40.67 dB, 38.72 dB, and 37.40 dB, respectively, all being significantly better than 36.84 dB using TV.

Statistical CT reconstruction using region-aware texture preserving regularization learning from prior normal-dose CT image

In some clinical applications, prior normal-dose CT (NdCT) images are available, and the valuable textures and structure features in them may be used to promote follow-up low-dose CT (LdCT) reconstruction. This study aims to learn texture information from the NdCT images and leverage it for follow-up LdCT image reconstruction to preserve textures and structure features. Specifically, the proposed reconstruction method first learns the texture information from those patches with similar structures in NdCT image, and the similar patches can be clustered by searching context features efficiently from the surroundings of the current patch. Then it utilizes redundant texture information from the similar patches as a priori knowledge to describe specific regions in the LdCT image. The advanced region-aware texture preserving prior is termed as 'RATP'. The main advantage of the PATP prior is that it can properly learn the texture features from available NdCT images and adaptively characterize the region-specific structures in the LdCT image. The experiments using patient data were performed to evaluate the performance of the proposed method. The proposed RATP method demonstrated superior performance in LdCT imaging compared to the filtered back projection (FBP) and statistical iterative reconstruction (SIR) methods using Gaussian regularization, Huber regularization and the original texture preserving regularization.

Registration-based multi-orientation tomography

We propose a combination of an experimental approach and a reconstruction technique that leads to reduction of artefacts in X-ray computer tomography of strongly attenuating objects. Through fully automatic data alignment, data generated in multiple experiments with varying object orientations are combined. Simulations and experiments show that the solutions computed using algebraic methods based on multiple acquisitions can achieve a dramatic improvement in the reconstruction quality, even when each acquisition generates a reduced number of projections. The approach does not require any advanced setup components making it ideal for laboratory-based X-ray tomography.

Regularization strategies in statistical image reconstruction of low-dose x-ray CT: A review

Statistical image reconstruction (SIR) methods have shown potential to substantially improve the image quality of low-dose x-ray computed tomography (CT) as compared to the conventional filtered back-projection (FBP) method. According to the maximum a posteriori (MAP) estimation, the SIR methods are typically formulated by an objective function consisting of two terms: (a) a data-fidelity term that models imaging geometry and physical detection processes in projection data acquisition, and (b) a regularization term that reflects prior knowledge or expectations of the characteristics of the to-be-reconstructed image. SIR desires accurate system modeling of data acquisition, while the regularization term also has a strong influence on the quality of reconstructed images. A variety of regularization strategies have been proposed for SIR in the past decades, based on different assumptions, models, and prior knowledge. In this paper, we review the conceptual and mathematical bases of these regularization strategies and briefly illustrate their efficacies in SIR of low-dose CT.

Unmixing dynamic PET images with variable specific binding kinetics

To analyze dynamic positron emission tomography (PET) images, various generic multivariate data analysis techniques have been considered in the literature, such as principal component analysis (PCA), independent component analysis (ICA), factor analysis and nonnegative matrix factorization (NMF). Nevertheless, these conventional approaches neglect any possible nonlinear variations in the time activity curves describing the kinetic behavior of tissues with specific binding, which limits their ability to recover a reliable, understandable and interpretable description of the data. This paper proposes an alternative analysis paradigm that accounts for spatial fluctuations in the exchange rate of the tracer between a free compartment and a specifically bound ligand compartment. The method relies on the concept of linear unmixing, usually applied on the hyperspectral domain, which combines NMF with a sum-to-one constraint that ensures an exhaustive description of the mixtures. The spatial variability of the signature corresponding to the specific binding tissue is explicitly modeled through a perturbed component. The performance of the method is assessed on both synthetic and real data and is shown to compete favorably when compared to other conventional analysis methods.

Reconstruction-of-difference (RoD) imaging for cone-beam CT neuro-angiography

Timely evaluation of neurovasculature via CT angiography (CTA) is critical to the detection of pathology such as ischemic stroke. Cone-beam CTA (CBCT-A) systems provide potential advantages in the timely use at the point-of-care, although challenges of a relatively slow gantry rotation speed introduce tradeoffs among image quality, data consistency and data sparsity. This work describes and evaluates a new reconstruction-of-difference (RoD) approach that is robust to such challenges. A fast digital simulation framework was developed to test the performance of the RoD over standard reference reconstruction methods such as filtered back-projection (FBP) and penalized likelihood (PL) over a broad range of imaging conditions, grouped into three scenarios to test the trade-off between data consistency, data sparsity and peak contrast. Two experiments were also conducted using a CBCT prototype and an anthropomorphic neurovascular phantom to test the simulation findings in real data. Performance was evaluated primarily in terms of normalized root mean square error (NRMSE) in comparison to truth, with reconstruction parameters chosen to optimize performance in each case to ensure fair comparison. The RoD approach reduced NRMSE in reconstructed images by up to 50%-53% compared to FBP and up to 29%-31% compared to PL for each scenario. Scan protocols well suited to the RoD approach were identified that balance tradeoffs among data consistency, sparsity and peak contrast-for example, a CBCT-A scan with 128 projections acquired in 8.5 s over a 180°  +  fan angle half-scan for a time attenuation curve with ~8.5 s time-to-peak and 600 HU peak contrast. With imaging conditions such as the simulation scenarios of fixed data sparsity (i.e. varying levels of data consistency and peak contrast), the experiments confirmed the reduction of NRMSE by 34% and 17% compared to FBP and PL, respectively. The RoD approach demonstrated superior performance in 3D angiography compared to FBP and PL in all simulation and physical experiments, suggesting the possibility of CBCT-A on low-cost, mobile imaging platforms suitable to the point-of-care. The algorithm demonstrated accurate reconstruction with a high degree of robustness against data sparsity and inconsistency.

Advances in PET/MR instrumentation and image reconstruction

The combination of positron emission tomography (PET) and MRI has attracted the attention of researchers in the past approximately 20 years in small-animal imaging and more recently in clinical research. The combination of PET/MRI allows researchers to explore clinical and research questions in a wide number of fields, some of which are briefly mentioned here. An important number of groups have developed different concepts to tackle the problems that PET instrumentation poses to the exposition of electromagnetic fields. We have described most of these research developments in preclinical and clinical experiments, including the few commercial scanners available. From the software perspective, an important number of algorithms have been developed to address the attenuation correction issue and to exploit the possibility that MRI provides for motion correction and quantitative image reconstruction, especially parametric modelling of radiopharmaceutical kinetics. In this work, we give an overview of some exemplar applications of simultaneous PET/MRI, together with technological hardware and software developments.

GPU-based Branchless Distance-Driven Projection and Backprojection

Projection and backprojection operations are essential in a variety of image reconstruction and physical correction algorithms in CT. The distance-driven (DD) projection and backprojection are widely used for their highly sequential memory access pattern and low arithmetic cost. However, a typical DD implementation has an inner loop that adjusts the calculation depending on the relative position between voxel and detector cell boundaries. The irregularity of the branch behavior makes it inefficient to be implemented on massively parallel computing devices such as graphics processing units (GPUs). Such irregular branch behaviors can be eliminated by factorizing the DD operation as three branchless steps: integration, linear interpolation, and differentiation, all of which are highly amenable to massive vectorization. In this paper, we implement and evaluate a highly parallel branchless DD algorithm for 3D cone beam CT. The algorithm utilizes the texture memory and hardware interpolation on GPUs to achieve fast computational speed. The developed branchless DD algorithm achieved 137-fold speedup for forward projection and 188-fold speedup for backprojection relative to a single-thread CPU implementation. Compared with a state-of-the-art 32-thread CPU implementation, the proposed branchless DD achieved 8-fold acceleration for forward projection and 10-fold acceleration for backprojection. GPU based branchless DD method was evaluated by iterative reconstruction algorithms with both simulation and real datasets. It obtained visually identical images as the CPU reference algorithm.

Low-Dose CBCT Reconstruction Using Hessian Schatten Penalties

Cone-beam computed tomography (CBCT) has been widely used in radiation therapy. For accurate patient setup and treatment target localization, it is important to obtain high-quality reconstruction images. The total variation (TV) penalty has shown the state-of-the-art performance in suppressing noise and preserving edges for statistical iterative image reconstruction, but it sometimes leads to the so-called staircase effect. In this paper, we proposed to use a new family of penalties-the Hessian Schatten (HS) penalties-for the CBCT reconstruction. Consisting of the second-order derivatives, the HS penalties are able to reflect the smooth intensity transitions of the underlying image without introducing the staircase effect. We discussed and compared the behaviors of several convex HS penalties with orders 1, 2, and for CBCT reconstruction. We used the majorization-minimization approach with a primal-dual formulation for the corresponding optimization problem. Experiments on two digital phantoms and two physical phantoms demonstrated the proposed penalty family's outstanding performance over TV in suppressing the staircase effect, and the HS penalty with order 1 had the best performance among the HS penalties tested.

Improved Simultaneous Algebraic Reconstruction Technique Algorithm for Positron-Emission Tomography Image Reconstruction via Minimizing the Fast Total Variation

CONTEXT

There has been considerable progress in the instrumentation for data measurement and computer methods for generating images of measured PET data. These computer methods have been developed to solve the inverse problem, also known as the "image reconstruction from projections" problem.

AIM

In this paper, we propose a modified Simultaneous Algebraic Reconstruction Technique (SART) algorithm to improve the quality of image reconstruction by incorporating total variation (TV) minimization into the iterative SART algorithm.

METHODOLOGY

The SART updates the estimated image by forward projecting the initial image onto the sinogram space. Then, the difference between the estimated sinogram and the given sinogram is back-projected onto the image domain. This difference is then subtracted from the initial image to obtain a corrected image. Fast total variation (FTV) minimization is applied to the image obtained in the SART step. The second step is the result obtained from the previous FTV update. The SART and the FTV minimization steps run iteratively in an alternating manner. Fifty iterations were applied to the SART algorithm used in each of the regularization-based methods. In addition to the conventional SART algorithm, spatial smoothing was used to enhance the quality of the image. All images were sized at 128 × 128 pixels.

RESULTS

The proposed algorithm successfully accomplished edge preservation. A detailed scrutiny revealed that the reconstruction algorithms differed; for example, the SART and the proposed FTV-SART algorithm effectively preserved the hot lesion edges, whereas artifacts and deviations were more likely to occur in the ART algorithm than in the other algorithms.

CONCLUSIONS

Compared to the standard SART, the proposed algorithm is more robust in removing background noise while preserving edges to suppress the existent image artifacts. The quality measurements and visual inspections show a significant improvement in image quality compared to the conventional SART and Algebraic Reconstruction Technique (ART) algorithms.