A unified approach to statistical tomography using coordinate descent optimization

Parameter-Free Multiview K-Means Clustering With Coordinate Descent Method

Recently, more and more real-world datasets have been composed of heterogeneous but related features from diverse views. Multiview clustering provides a promising attempt at a solution for partitioning such data according to heterogeneous information. However, most existing methods suffer from hyper-parameter tuning trouble and high computational cost. Besides, there is still an opportunity for improvement in clustering performance. To this end, a novel multiview framework, called parameter-free multiview -means clustering with coordinate descent method (PFMVKM), is presented to address the above problems. Specifically, PFMVKM is completely parameter-free and learns the weights via a self-weighted scheme, which can avoid the intractable process of hyper-parameters tuning. Moreover, our model is capable of directly calculating the cluster indicator matrix, with no need to learn the cluster centroid matrix and the indicator matrix simultaneously as previous multiview methods have to do. What's more, we propose an efficient optimization algorithm utilizing the idea of coordinate descent, which can not only reduce the computational complexity but also improve the clustering performance. Extensive experiments on various types of real datasets illustrate that the proposed method outperforms existing state-of-the-art competitors and conforms well with the actual situation.

Compressed-sensing-inspired reconstruction algorithms in low-dose computed tomography: A review

BACKGROUND

Optimization of the dose the patient receives during scanning is an important problem in modern medical X-ray computed tomography (CT). One of the basic ways to its solution is to reduce the number of views. Compressed sensing theory helped promote the development of a new class of effective reconstruction algorithms for limited data CT. These compressed-sensing-inspired (CSI) algorithms optimize the Lp (0 ≤ p ≤ 1) norm of images and can accurately reconstruct CT tomograms from a very few views. The paper presents a review of the CSI algorithms and discusses prospects for their further use in commercial low-dose CT.

METHODS

Many literature references with the CSI algorithms have been were searched. To structure the material collected the author gives a classification framework within which he describes Lp regularization methods, the basic CSI algorithms that are used most often in few-view CT, and some of their derivatives. Lots of examples are provided to illustrate the use of the CSI algorithms in few-view and low-dose CT.

RESULTS

A list of the CSI algorithms is compiled from the literature search. For better demonstrativeness they are summarized in a table. The inference is done that already today some of the algorithms are capable of reconstruction from 20 to 30 views with acceptable quality and dose reduction by a factor of 10.

DISCUSSION

In conclusion the author discusses how soon the CSI reconstruction algorithms can be introduced in the practice of medical diagnosis and used in commercial CT scanners.

Deep learning-based harmonization of trabecular bone microstructures between high- and low-resolution CT imaging

BACKGROUND

Osteoporosis is a bone disease related to increased bone loss and fracture-risk. The variability in bone strength is partially explained by bone mineral density (BMD), and the remainder is contributed by bone microstructure. Recently, clinical CT has emerged as a viable option for in vivo bone microstructural imaging. Wide variations in spatial-resolution and other imaging features among different CT scanners add inconsistency to derived bone microstructural metrics, urging the need for harmonization of image data from different scanners.

PURPOSE

This paper presents a new deep learning (DL) method for the harmonization of bone microstructural images derived from low- and high-resolution CT scanners and evaluates the method's performance at the levels of image data as well as derived microstructural metrics.

METHODS

We generalized a three-dimensional (3D) version of GAN-CIRCLE that applies two generative adversarial networks (GANs) constrained by the identical, residual, and cycle learning ensemble (CIRCLE). Two GAN modules simultaneously learn to map low-resolution CT (LRCT) to high-resolution CT (HRCT) and vice versa. Twenty volunteers were recruited. LRCT and HRCT scans of the distal tibia of their left legs were acquired. Five-hundred pairs of LRCT and HRCT image blocks of64 × 64 × 64 $64 \times 64 \times 64 $ voxels were sampled for each of the twelve volunteers and used for training in supervised as well as unsupervised setups. LRCT and HRCT images of the remaining eight volunteers were used for evaluation. LRCT blocks were sampled at 32 voxel intervals in each coordinate direction and predicted HRCT blocks were stitched to generate a predicted HRCT image.

RESULTS

Mean ± standard deviation of structural similarity (SSIM) values between predicted and true HRCT using both 3DGAN-CIRCLE-based supervised (0.84 ± 0.03) and unsupervised (0.83 ± 0.04) methods were significantly (p < 0.001) higher than the mean SSIM value between LRCT and true HRCT (0.75 ± 0.03). All Tb measures derived from predicted HRCT by the supervised 3DGAN-CIRCLE showed higher agreement (CCC  ∈ $ \in $ [0.956 0.991]) with the reference values from true HRCT as compared to LRCT-derived values (CCC  ∈ $ \in $ [0.732 0.989]). For all Tb measures, except Tb plate-width (CCC = 0.866), the unsupervised 3DGAN-CIRCLE showed high agreement (CCC  ∈ $ \in $ [0.920 0.964]) with the true HRCT-derived reference measures. Moreover, Bland-Altman plots showed that supervised 3DGAN-CIRCLE predicted HRCT reduces bias and variability in residual values of different Tb measures as compared to LRCT and unsupervised 3DGAN-CIRCLE predicted HRCT. The supervised 3DGAN-CIRCLE method produced significantly improved performance (p < 0.001) for all Tb measures as compared to the two DL-based supervised methods available in the literature.

CONCLUSIONS

3DGAN-CIRCLE, trained in either unsupervised or supervised fashion, generates HRCT images with high structural similarity to the reference true HRCT images. The supervised 3DGAN-CIRCLE improves agreements of computed Tb microstructural measures with their reference values and outperforms the unsupervised 3DGAN-CIRCLE. 3DGAN-CIRCLE offers a viable DL solution to retrospectively improve image resolution, which may aid in data harmonization in multi-site longitudinal studies where scanner mismatch is unavoidable.

Comparison of iterative reconstruction implementations for multislice helical CT

The most mature image reconstruction algorithms in multislice helical computed tomography are based on analytical and iterative methods. Over the past decades, several methods have been developed for iterative reconstructions that improve image quality by reducing noise and artifacts. In the regularization step of iterative reconstruction, noise can be significantly reduced, thereby making low-dose CT. The quality of the reconstructed image can be further improved by using model-based reconstructions. In these reconstructions, the main focus is on modeling the data acquisition process, including the behavior of the photon beams, the geometry of the system, etc. In this article, we propose two model-based reconstruction algorithms using a virtual detector for multislice helical CT. The aim of this study is to compare the effect of using a virtual detector on image quality for the two proposed algorithms with a model-based iterative reconstruction using the original detector model. Since the algorithms are implemented using multiple GPUs, the merging of separately reconstructed volumes can significantly affect image quality. This issue is often referred to as the "long object" problem, for which we also present a solution that plays an important role in the proposed reconstruction processes. The algorithms were evaluated using mathematical and physical phantoms, as well as patient cases. The SSIM, MS-SSIM and L1 metrics were utilized to evaluate the image quality of the mathematical phantom case. To demonstrate the effectiveness of the algorithms, we used the CatPhan 600 phantom. Additionally, anonymized patient scans were used to showcase the improvements in image quality on real scan data.

Self-supervised denoising of projection data for low-dose cone-beam CT

BACKGROUND

Convolutional neural networks (CNNs) have shown promising results in image denoising tasks. While most existing CNN-based methods depend on supervised learning by directly mapping noisy inputs to clean targets, high-quality references are often unavailable for interventional radiology such as cone-beam computed tomography (CBCT).

PURPOSE

In this paper, we propose a novel self-supervised learning method that reduces noise in projections acquired by ordinary CBCT scans.

METHODS

With a network that partially blinds input, we are able to train the denoising model by mapping the partially blinded projections to the original projections. Additionally, we incorporate noise-to-noise learning into the self-supervised learning by mapping the adjacent projections to the original projections. With standard image reconstruction methods such as FDK-type algorithms, we can reconstruct high-quality CBCT images from the projections denoised by our projection-domain denoising method.

RESULTS

In the head phantom study, we measure peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM) values of the proposed method along with the other denoising methods and uncorrected low-dose CBCT data for a quantitative comparison both in projection and image domains. The PSNR and SSIM values of our self-supervised denoising approach are 27.08 and 0.839, whereas those of uncorrected CBCT images are 15.68 and 0.103, respectively. In the retrospective study, we assess the quality of interventional patient CBCT images to evaluate the projection-domain and image-domain denoising methods. Both qualitative and quantitative results indicate that our approach can effectively produce high-quality CBCT images with low-dose projections in the absence of duplicate clean or noisy references.

CONCLUSIONS

Our self-supervised learning strategy is capable of restoring anatomical information while efficiently removing noise in CBCT projection data.

Deep learning-based image reconstruction and post-processing methods in positron emission tomography for low-dose imaging and resolution enhancement

Image processing plays a crucial role in maximising diagnostic quality of positron emission tomography (PET) images. Recently, deep learning methods developed across many fields have shown tremendous potential when applied to medical image enhancement, resulting in a rich and rapidly advancing literature surrounding this subject. This review encapsulates methods for integrating deep learning into PET image reconstruction and post-processing for low-dose imaging and resolution enhancement. A brief introduction to conventional image processing techniques in PET is firstly presented. We then review methods which integrate deep learning into the image reconstruction framework as either deep learning-based regularisation or as a fully data-driven mapping from measured signal to images. Deep learning-based post-processing methods for low-dose imaging, temporal resolution enhancement and spatial resolution enhancement are also reviewed. Finally, the challenges associated with applying deep learning to enhance PET images in the clinical setting are discussed and future research directions to address these challenges are presented.

Low-dose cone-beam computed tomography reconstruction through a fast three-dimensional compressed sensing method based on the three-dimensional pseudo-polar fourier transform

Background:

Reconstruction of high quality two dimensional images from fan beam computed tomography (CT) with a limited number of projections is already feasible through Fourier based iterative reconstruction method. However, this article is focused on a more complicated reconstruction of three dimensional (3D) images in a sparse view cone beam computed tomography (CBCT) by utilizing Compressive Sensing (CS) based on 3D pseudo polar Fourier transform (PPFT).

Method:

In comparison with the prevalent Cartesian grid, PPFT re gridding is potent to remove rebinning and interpolation errors. Furthermore, using PPFT based radon transform as the measurement matrix, reduced the computational complexity.

Results:

In order to show the computational efficiency of the proposed method, we compare it with an algebraic reconstruction technique and a CS type algorithm. We observed convergence in <20 iterations in our algorithm while others would need at least 50 iterations for reconstructing a qualified phantom image. Furthermore, using a fast composite splitting algorithm solver in each iteration makes it a fast CBCT reconstruction algorithm. The algorithm will minimize a linear combination of three terms corresponding to a least square data fitting, Hessian (HS) Penalty and l1 norm wavelet regularization. We named it PP-based compressed sensing-HS-W. In the reconstruction range of 120 projections around the 360° rotation, the image quality is visually similar to reconstructed images by Feldkamp-Davis-Kress algorithm using 720 projections. This represents a high dose reduction.

Conclusion:

The main achievements of this work are to reduce the radiation dose without degrading the image quality. Its ability in removing the staircase effect, preserving edges and regions with smooth intensity transition, and producing high-resolution, low-noise reconstruction results in low-dose level are also shown.

A New Statistical Reconstruction Method for the Computed Tomography Using an X-Ray Tube with Flying Focal Spot

This paper presents a new image reconstruction method for spiral cone- beam tomography scanners in which an X-ray tube with a flying focal spot is used. The method is based on principles related to the statistical model-based iterative reconstruction (MBIR) methodology. The proposed approach is a continuous-to-continuous data model approach, and the forward model is formulated as a shift-invariant system. This allows for avoiding a nutating reconstruction-based approach, e.g. the advanced single slice rebinning methodology (ASSR) that is usually applied in computed tomography (CT) scanners with X-ray tubes with a flying focal spot. In turn, the proposed approach allows for significantly accelerating the reconstruction processing and, generally, for greatly simplifying the entire reconstruction procedure. Additionally, it improves the quality of the reconstructed images in comparison to the traditional algorithms, as confirmed by extensive simulations. It is worth noting that the main purpose of introducing statistical reconstruction methods to medical CT scanners is the reduction of the impact of measurement noise on the quality of tomography images and, consequently, the dose reduction of X-ray radiation absorbed by a patient. A series of computer simulations followed by doctor’s assessments have been performed, which indicate how great a reduction of the absorbed dose can be achieved using the reconstruction approach presented here.

Multi-Objective Evolutionary Algorithm for PET Image Reconstruction: Concept

In many diagnostic imaging settings, including positron emission tomography (PET), images are typically used for multiple tasks such as detecting disease and quantifying disease. Unlike conventional image reconstruction that optimizes a single objective, this work proposes a multi-objective optimization algorithm for PET image reconstruction to identify a set of images that are optimal for more than one task. This work is reliant on a genetic algorithm to evolve a set of solutions that satisfies two distinct objectives. In this paper, we defined the objectives as the commonly used Poisson log-likelihood function, typically reflective of quantitative accuracy, and a variant of the generalized scan-statistic model, to reflect detection performance. The genetic algorithm uses new mutation and crossover operations at each iteration. After each iteration, the child population is selected with non-dominated sorting to identify the set of solutions along the dominant front or fronts. After multiple iterations, these fronts approach a single non-dominated optimal front, defined as the set of PET images for which none the objective function values can be improved without reducing the opposing objective function. This method was applied to simulated 2D PET data of the heart and liver with hot features. We compared this approach to conventional, single-objective approaches for trading off performance: maximum likelihood estimation with increasing explicit regularization and maximum a posteriori estimation with varying penalty strength. Results demonstrate that the proposed method generates solutions with comparable to improved objective function values compared to the conventional approaches for trading off performance amongst different tasks. In addition, this approach identifies a diverse set of solutions in the multi-objective function space which can be challenging to estimate with single-objective formulations.

PWLS-PR: low-dose computed tomography image reconstruction using a patch-based regularization method based on the penalized weighted least squares total variation approach

BACKGROUND

Radiation exposure computed tomography (CT) scans and the associated risk of cancer in patients have been major clinical concerns. Existing research can achieve low-dose CT imaging by reducing the X-ray current and the number of projections per rotation of the human body. However, this method may produce excessive noise and fringe artifacts in the traditional filtered back projection (FBP)-reconstructed image.

METHODS

To solve this problem, iterative image reconstruction is a promising option to obtain high-quality images from low-dose scans. This paper proposes a patch-based regularization method based on penalized weighted least squares total variation (PWLS-PR) for iterative image reconstruction. This method uses neighborhood patches instead of single pixels to calculate the nonquadratic penalty. The proposed regularization method is more robust than the conventional regularization method in identifying random fluctuations caused by sharp edges and noise. Each iteration of the proposed algorithm can be described in the following three steps: image updating via the total variation based on penalized weighted least squares (PWLS-TV), image smoothing, and pixel-by-pixel image fusion.

RESULTS

Simulation and real-world projection experiments show that the proposed PWLS-PR algorithm achieves a higher image reconstruction performance than similar algorithms. Through the qualitative and quantitative evaluation of simulation experiments, the effectiveness of the method is also verified.

CONCLUSIONS

Furthermore, this study shows that the PWLS-PR method reduces the amount of projection data required for repeated CT scans and has the useful potential to reduce the radiation dose in clinical medical applications.

A Novel Low-Dose Dual-Energy Imaging Method for a Fast-Rotating Gantry-Type CT Scanner

CT scan by use of a beam-filter placed between the x-ray source and the patient allows a single-scan low-dose dual-energy imaging with a minimal hardware modification to the existing CT systems. We have earlier demonstrated the feasibility of such imaging method with a multi-slit beam-filter reciprocating along the direction perpendicular to the CT rotation axis in a cone-beam CT system. However, such method would face mechanical challenges when the beam-filter is supposed to cooperate with a fast-rotating gantry in a diagnostic CT system. In this work, we propose a new scanning method and associated image reconstruction algorithm that can overcome these challenges. We propose to slide a beam-filter that has multi-slit structure with its slits being at a slanted angle with the CT gantry rotation axis during a scan. A streaky pattern would show up in the sinogram domain as a result. Using a notch filter in the Fourier domain of the sinogram, we removed the streaks and reconstructed an image by use of the filtered-backprojection algorithm. The remaining image artifacts were suppressed by applying l₀ norm based smoothing. Using this image as a prior, we have reconstructed low- and high-energy CT images in the iterative reconstruction framework. An image-based material decomposition then followed. We conducted a simulation study to test its feasibility using the XCAT phantom and also an experimental study using the Catphan phantom, a head phantom, an iodine-solution phantom, and a monkey in anesthesia, and showed its successful performance in image reconstruction and in material decomposition.

Generative adversarial network-based sinogram super-resolution for computed tomography imaging

Compared with the conventional 1×1 acquisition mode of projection in computed tomography (CT) image reconstruction, the 2×2 acquisition mode improves the collection efficiency of the projection and reduces the x-ray exposure time. However, the collected projection based on the 2×2 acquisition mode has low resolution (LR) and the reconstructed image quality is poor, thus limiting the use of this mode in CT imaging systems. In this study, a novel sinogram-super-resolution (SR) generative adversarial network model is proposed to obtain high-resolution (HR) sinograms from LR sinograms, thereby improving the reconstruction image quality under the 2×2 acquisition mode. The proposed generator is based on the residual network for LR sinogram feature extraction and SR sinogram generation. A relativistic discriminator is designed to render the network capable of obtaining more realistic SR sinograms. Moreover, we combine the cycle consistency loss, sinogram domain loss, and reconstruction image domain loss in the total loss function to supervise SR sinogram generation. Then, a trained model can be obtained by inputting the paired LR/HR sinograms into the network. Finally, the classic filtered-back-projection reconstruction algorithm is used for CT image reconstruction based on the generated SR sinogram. The qualitative and quantitative results of evaluations on digital and real data illustrate that the proposed model not only obtains clean SR sinograms from noisy LR sinograms but also outperforms its counterparts.

Low-dose CT image and projection dataset

PURPOSE

To describe a large, publicly available dataset comprising computed tomography (CT) projection data from patient exams, both at routine clinical doses and simulated lower doses.

ACQUISITION AND VALIDATION METHODS

The library was developed under local ethics committee approval. Projection and image data from 299 clinically performed patient CT exams were archived for three types of clinical exams: noncontrast head CT scans acquired for acute cognitive or motor deficit, low-dose noncontrast chest scans acquired to screen high-risk patients for pulmonary nodules, and contrast-enhanced CT scans of the abdomen acquired to look for metastatic liver lesions. Scans were performed on CT systems from two different CT manufacturers using routine clinical protocols. Projection data were validated by reconstructing the data using several different reconstruction algorithms and through use of the data in the 2016 Low Dose CT Grand Challenge. Reduced dose projection data were simulated for each scan using a validated noise-insertion method. Radiologists marked location and diagnosis for detected pathologies. Reference truth was obtained from the patient medical record, either from histology or subsequent imaging.

DATA FORMAT AND USAGE NOTES

Projection datasets were converted into the previously developed DICOM-CT-PD format, which is an extended DICOM format created to store CT projections and acquisition geometry in a nonproprietary format. Image data are stored in the standard DICOM image format and clinical data in a spreadsheet. Materials are provided to help investigators use the DICOM-CT-PD files, including a dictionary file, data reader, and user manual. The library is publicly available from The Cancer Imaging Archive (https://doi.org/10.7937/9npb-2637).

POTENTIAL APPLICATIONS

This CT data library will facilitate the development and validation of new CT reconstruction and/or denoising algorithms, including those associated with machine learning or artificial intelligence. The provided clinical information allows evaluation of task-based diagnostic performance.

A Practical Statistical Approach to the Reconstruction Problem Using a Single Slice Rebinning Method

The paper presented here describes a new practical approach to the reconstruction problem applied to 3D spiral x-ray tomography. The concept we propose is based on a continuous-to-continuous data model, and the reconstruction problem is formulated as a shift invariant system. This original reconstruction method is formulated taking into consideration the statistical properties of signals obtained by the 3D geometry of a CT scanner. It belongs to the class of nutating reconstruction methods and is based on the advanced single slice rebinning (ASSR) methodology. The concept shown here significantly improves the quality of the images obtained after reconstruction and decreases the complexity of the reconstruction problem in comparison with other approaches. Computer simulations have been performed, which prove that the reconstruction algorithm described here does indeed significantly outperforms conventional analytical methods in the quality of the images obtained.

Far-field thermal imaging below diffraction limit

Non-uniform self-heating and temperature hotspots are major concerns compromising the performance and reliability of submicron electronic and optoelectronic devices. At deep submicron scales where effects such as contact-related artifacts and diffraction limits accurate measurements of temperature hotspots, non-contact thermal characterization can be extremely valuable. In this work, we use a Bayesian optimization framework with generalized Gaussian Markov random field (GGMRF) prior model to obtain accurate full-field temperature distribution of self-heated metal interconnects from their thermoreflectance thermal images (TRI) with spatial resolution 2.5 times below Rayleigh limit for 530nm illumination. Finite element simulations along with TRI experimental data were used to characterize the point spread function of the optical imaging system. In addition, unlike iterative reconstruction algorithms that use ad hoc regularization parameters in their prior models to obtain the best quality image, we used numerical experiments and finite element modeling to estimate the regularization parameter for solving a real experimental inverse problem.

Deep Learning Based High-Resolution Reconstruction of Trabecular Bone Microstructures from Low-Resolution CT Scans using GAN-CIRCLE

Osteoporosis is a common age-related disease characterized by reduced bone density and increased fracture-risk. Microstructural quality of trabecular bone (Tb), commonly found at axial skeletal sites and at the end of long bones, is an important determinant of bone-strength and fracture-risk. High-resolution emerging CT scanners enable in vivo measurement of Tb microstructures at peripheral sites. However, resolution-dependence of microstructural measures and wide resolution-discrepancies among various CT scanners together with rapid upgrades in technology warrant data harmonization in CT-based cross-sectional and longitudinal bone studies. This paper presents a deep learning-based method for high-resolution reconstruction of Tb microstructures from low-resolution CT scans using GAN-CIRCLE. A network was developed and evaluated using post-registered ankle CT scans of nineteen volunteers on both low- and high-resolution CT scanners. 9,000 matching pairs of low- and high-resolution patches of size 64×64 were randomly harvested from ten volunteers for training and validation. Another 5,000 matching pairs of patches from nine other volunteers were used for evaluation. Quantitative comparison shows that predicted high-resolution scans have significantly improved structural similarity index (p < 0.01) with true high-resolution scans as compared to the same metric for low-resolution data. Different Tb microstructural measures such as thickness, spacing, and network area density are also computed from low- and predicted high-resolution images, and compared with the values derived from true high-resolution scans. Thickness and network area measures from predicted images showed higher agreement with true high-resolution CT (CCC = [0.95, 0.91]) derived values than the same measures from low-resolution images (CCC = [0.72, 0.88]).

Review of CT image reconstruction open source toolkits

Computed tomography (CT) has been widely applied in medical diagnosis, nondestructive evaluation, homeland security, and other science and engineering applications. Image reconstruction is one of the core CT imaging technologies. In this review paper, we systematically reviewed the currently publicly available CT image reconstruction open source toolkits in the aspects of their environments, object models, imaging geometries, and algorithms. In addition to analytic and iterative algorithms, deep learning reconstruction networks and open codes are also reviewed as the third category of reconstruction algorithms. This systematic summary of the publicly available software platforms will help facilitate CT research and development.

CT Super-Resolution GAN Constrained by the Identical, Residual, and Cycle Learning Ensemble (GAN-CIRCLE)

In this paper, we present a semi-supervised deep learning approach to accurately recover high-resolution (HR) CT images from low-resolution (LR) counterparts. Specifically, with the generative adversarial network (GAN) as the building block, we enforce the cycle-consistency in terms of the Wasserstein distance to establish a nonlinear end-to-end mapping from noisy LR input images to denoised and deblurred HR outputs. We also include the joint constraints in the loss function to facilitate structural preservation. In this process, we incorporate deep convolutional neural network (CNN), residual learning, and network in network techniques for feature extraction and restoration. In contrast to the current trend of increasing network depth and complexity to boost the imaging performance, we apply a parallel 1×1 CNN to compress the output of the hidden layer and optimize the number of layers and the number of filters for each convolutional layer. The quantitative and qualitative evaluative results demonstrate that our proposed model is accurate, efficient and robust for super-resolution (SR) image restoration from noisy LR input images. In particular, we validate our composite SR networks on three large-scale CT datasets, and obtain promising results as compared to the other state-of-the-art methods.

Joint image reconstruction and segmentation: Comparison of two algorithms for few-view tomography

Two algorithms of few-view tomography are compared, specifically, the iterative Potts minimization algorithm (IPMA) and the algebraic reconstruction technique with TV-regularization and adaptive segmentation (ART-TVS). Both aim to reconstruct piecewise-constant structures, use the compressed sensing theory, and combine image reconstruction and segmentation procedures. Using a numerical experiment, it is shown that either algorithm can exactly reconstruct the Shepp-Logan phantom from as small as 7 views with noise characteristic of the medical applications of X-ray tomography. However, if an object has a complicated high-frequency structure (QR-code), the minimal number of views required for its exact reconstruction increases to 17–21 for ART-TVS and to 32–34 for IPMA. The ART-TVS algorithm developed by the authors is shown to outperform IPMA in reconstruction accuracy and speed and in resistance to abnormally high noise as well. ART-TVS holds good potential for further improvement.

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.

Limited-View X-Ray Tomography Combining Attenuation and Compton Scatter Data: Approach and Experimental Results

X-ray inspection systems are critical in medical, non-destructive testing, and security applications, with systems typically measuring attenuation along straight-line paths connecting sources and detectors. Computed tomography (CT) systems can provide higher-quality images than single- or dual-view systems, but the need to measure many projections leads to greater system cost and complexity. Typically, off-angle Compton scattered photons are treated as noise during tomographic inversion. We seek to maximize the image quality of limited-view systems by combining attenuation data with measurements of Compton-scattered photons, exploiting the fact that the broken-ray paths followed by scattered photons provide additional geometric sampling of the scene. We describe a single-scatter forward model for Compton-scatter data measured with energy-resolving detectors, and demonstrate a reconstruction algorithm for density that combines both attenuation and scatter measurements. The experimental results suggest that including Compton-scattered data in the reconstruction process can improve image quality for density reconstruction using limited-view systems.

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.

Quantitative susceptibility map reconstruction using annihilating filter-based low-rank Hankel matrix approach

PURPOSE

Quantitative susceptibility mapping (QSM) inevitably suffers from streaking artifacts caused by zeros on the conical surface of the dipole kernel in k-space. This work proposes a novel and accurate QSM reconstruction method based on k-space low-rank Hankel matrix constraint, avoiding the over-smoothing problem and streaking artifacts.

THEORY AND METHODS

Based on the recent theory of annihilating filter-based low-rank Hankel matrix approach (ALOHA), QSM is formulated as deconvolution under low-rank Hankel matrix constraint in the k-space. The computational complexity and the high memory burden were reduced by successive reconstruction of 2-D planes along 3 independent axes of the 3-D phase image in Fourier domain. Feasibility of the proposed method was tested on a simulated phantom and human data and were compared with existing QSM reconstruction methods.

RESULTS

The proposed ALOHA-QSM effectively reduced streaking artifacts and accurately estimated susceptibility values in deep gray matter structures, compared to the existing QSM methods.

CONCLUSIONS

The suggested ALOHA-QSM algorithm successfully solves the 3-dimensional QSM dipole inversion problem using k-space low rank property with no anatomical constraint. ALOHA-QSM can provide detailed brain structures and accurate susceptibility values with no streaking artifacts.

Single-frequency LADAR super-resolution Doppler tomography for extended targets

Doppler tomography is an important means to obtain two-dimensional (2-D) images of remote targets. It is especially suitable for imaging spinning targets such as space debris, warheads, and aircraft blades. However, related research is mostly focused on the microwave band rather than the laser. Higher resolution can be achieved by implementing Doppler tomography in the laser band compared to the existing Doppler tomography in the microwave. Moreover, existing imaging methods are mostly directed at point targets. When these methods deal with extended target echoes, the image quality is unsatisfactory. These problems severely limit the application of Doppler tomography. Here, a novel laser Doppler tomography method has been proposed. The method is based on a single-frequency laser radar (LADAR) that does not require any form of wideband modulation of the transmitted signal. The imaging process is based on the precise relationship between the scattering coefficient of the target and the statistical characteristics of the Doppler spectrum and finds the maximum a posteriori (MAP) estimate of the scattering coefficient distribution. The imaging resolution depends on the Doppler frequency resolution, which exceeds the diffraction limit and is independent of the imaging distance. A laser Doppler tomography experimental system was established. With this system, high-quality laser Doppler tomograms of extended targets were obtained for the first time. In the experiment, the targets have different rotational speeds from 100 to 1000 r/min. The images of these targets with a resolution of 0.4 mm are obtained at a distance of 5 m indoors. In these images, the target details such as textures on the surfaces can be rendered. The quality of these images is greatly improved compared to existing processing methods. The experimental results confirm the effectiveness of the proposed laser Doppler tomography method.

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.

Permuted Coordinate-wise Optimizations Applied to Lp-regularized Image Deconvolution

Image deconvolution is an ill-posed problem that usually requires prior knowledge for regularizing the feasible solutions. In literature, iterative methods estimate an intrinsic image, minimizing a cost function regularized by specific prior information. However, it is difficult to directly minimize the constrained cost function, if a nondifferentiable regularization (e.g., the sparsity constraint) is employed. In this paper, we propose a nonderivative image deconvolution algorithm that solves the under-constrained problem (i.e., a non-blind image deconvolution) by successively solving the permuted subproblems. The subproblems, arranged in permuted sequences, directly minimize the nondifferentiable cost functions. Various Lp-regularized (0 < p ≤ 1, p = 2) objective functions are utilized to demonstrate the pixel-wise optimization, in which the projection operator generates simplified, low-dimensional subproblems for estimating each pixel. The subproblems, after projection, are dealt with in the corresponding hyperplanes containing the adjacent pixels of each image coordinate. Furthermore, successively solving the subproblems can accelerate the deconvolution process with a linear speed-up, by parallelizing the subproblem sequences. The image deconvolution results with various regularization functionals are presented and the linear speed-up is also demonstrated with a parallelized version of the proposed algorithm. Experimental results demonstrate that the proposed method outperforms the conventional methods in terms of the improved-signal-to-noise ratio and structural similarity index measure.

Spectroscopic stimulated Raman scattering imaging of highly dynamic specimens through matrix completion

Spectroscopic stimulated Raman scattering (SRS) imaging generates chemical maps of intrinsic molecules, with no need for prior knowledge. Despite great advances in instrumentation, the acquisition speed for a spectroscopic SRS image stack is fundamentally bounded by the pixel integration time. In this work, we report three-dimensional sparsely sampled spectroscopic SRS imaging that measures ~20% of pixels throughout the stack. In conjunction with related work in low-rank matrix completion (e.g., the Netflix Prize), we develop a regularized non-negative matrix factorization algorithm to decompose the sub-sampled image stack into spectral signatures and concentration maps. This design enables an acquisition speed of 0.8 s per image stack, with 50 frames in the spectral domain and 40,000 pixels in the spatial domain, which is faster than the conventional raster laser-scanning scheme by one order of magnitude. Such speed allows real-time metabolic imaging of living fungi suspended in a growth medium while effectively maintaining the spatial and spectral resolutions. This work is expected to promote broad application of matrix completion in spectroscopic laser-scanning imaging.

Discriminative Feature Representation to Improve Projection Data Inconsistency for Low Dose CT Imaging

In low dose computed tomography (LDCT) imaging, the data inconsistency of measured noisy projections can significantly deteriorate reconstruction images. To deal with this problem, we propose here a new sinogram restoration approach, the sinogram- discriminative feature representation (S-DFR) method. Different from other sinogram restoration methods, the proposed method works through a 3-D representation-based feature decomposition of the projected attenuation component and the noise component using a well-designed composite dictionary containing atoms with discriminative features. This method can be easily implemented with good robustness in parameter setting. Its comparison to other competing methods through experiments on simulated and real data demonstrated that the S-DFR method offers a sound alternative in LDCT.

Direct Reconstruction of CT-based Attenuation Correction Images for PET with Cluster-Based Penalties

Extremely low-dose CT acquisitions used for PET attenuation correction have high levels of noise and potential bias artifacts due to photon starvation. This work explores the use of a priori knowledge for iterative image reconstruction of the CT-based attenuation map. We investigate a maximum a posteriori framework with cluster-based multinomial penalty for direct iterative coordinate decent (dICD) reconstruction of the PET attenuation map. The objective function for direct iterative attenuation map reconstruction used a Poisson log-likelihood data fit term and evaluated two image penalty terms of spatial and mixture distributions. The spatial regularization is based on a quadratic penalty. For the mixture penalty, we assumed that the attenuation map may consist of four material clusters: air+background, lung, soft tissue, and bone. Using simulated noisy sinogram data, dICD reconstruction was performed with different strengths of the spatial and mixture penalties. The combined spatial and mixture penalties reduced the RMSE by roughly 2 times compared to a weighted least square and filtered backprojection reconstruction of CT images. The combined spatial and mixture penalties resulted in only slightly lower RMSE compared to a spatial quadratic penalty alone. For direct PET attenuation map reconstruction from ultra-low dose CT acquisitions, the combination of spatial and mixture penalties offers regularization of both variance and bias and is a potential method to reconstruct attenuation maps with negligible patient dose. The presented results, using a best-case histogram suggest that the mixture penalty does not offer a substantive benefit over conventional quadratic regularization and diminishes enthusiasm for exploring future application of the mixture penalty.

Comparison Between Pre-Log and Post-Log Statistical Models in Ultra-Low-Dose CT Reconstruction

X-ray detectors in clinical computed tomography (CT) usually operate in current-integrating mode. Their complicated signal statistics often lead to intractable likelihood functions for practical use in model-based image reconstruction (MBIR). It is therefore desirable to design simplified statistical models without losing the essential factors. Depending on whether the CT transmission data are logarithmically transformed, pre-log and post-log models are two major categories of choices in CT MBIR. Both being approximations, it remains an open question whether one model can notably improve image quality over the other on real scanners. In this study, we develop and compare several pre-log and post-log MBIR algorithms under a unified framework. Their reconstruction accuracy based on simulation and clinical datasets are evaluated. The results show that pre-log MBIR can achieve notably better quantitative accuracy than post-log MBIR in ultra-low-dose CT, although in less extreme cases, post-log MBIR with handcrafted pre-processing remains a competitive alternative. Pre-log MBIR could play a growing role in emerging ultra-low-dose CT applications.

Superiorization-based multi-energy CT image reconstruction

The recently-developed superiorization approach is efficient and robust for solving various constrained optimization problems. This methodology can be applied to multi-energy CT image reconstruction with the regularization in terms of the prior rank, intensity and sparsity model (PRISM). In this paper, we propose a superiorized version of the simultaneous algebraic reconstruction technique (SART) based on the PRISM model. Then, we compare the proposed superiorized algorithm with the Split-Bregman algorithm in numerical experiments. The results show that both the Superiorized-SART and the Split-Bregman algorithms generate good results with weak noise and reduced artefacts.

Modeling and Pre-Treatment of Photon-Starved CT Data for Iterative Reconstruction

An increasing number of X-ray CT procedures are being conducted with drastically reduced dosage, due at least in part to advances in statistical reconstruction methods that can deal more effectively with noise than can traditional techniques. As data become photon-limited, more detailed models are necessary to deal with count rates that drop to the levels of system electronic noise. We present two options for sinogram pre-treatment that can improve the performance of photon-starved measurements, with the intent of following with model-based image reconstruction. Both the local linear minimum mean-squared error (LLMMSE) filter and pointwise Bayesian restoration (PBR) show promise in extracting useful, quantitative information from very low-count data by reducing local bias while maintaining the lower noise variance of statistical methods. Results from clinical data demonstrate the potential of both techniques.

Measured PET Data Characterization with the Negative Binomial Distribution Model

Accurate statistical model of PET measurements is a prerequisite for a correct image reconstruction when using statistical image reconstruction algorithms, or when pre-filtering operations must be performed. Although radioactive decay follows a Poisson distribution, deviation from Poisson statistics occurs on projection data prior to reconstruction due to physical effects, measurement errors, correction of scatter and random coincidences. Modelling projection data can aid in understanding the statistical nature of the data in order to develop efficient processing methods and to reduce noise. This paper outlines the statistical behaviour of measured emission data evaluating the goodness of fit of the negative binomial (NB) distribution model to PET data for a wide range of emission activity values. An NB distribution model is characterized by the mean of the data and the dispersion parameter α that describes the deviation from Poisson statistics. Monte Carlo simulations were performed to evaluate: (a) the performances of the dispersion parameter α estimator, (b) the goodness of fit of the NB model for a wide range of activity values. We focused on the effect produced by correction for random and scatter events in the projection (sinogram) domain, due to their importance in quantitative analysis of PET data. The analysis developed herein allowed us to assess the accuracy of the NB distribution model to fit corrected sinogram data, and to evaluate the sensitivity of the dispersion parameter α to quantify deviation from Poisson statistics. By the sinogram ROI-based analysis, it was demonstrated that deviation on the measured data from Poisson statistics can be quantitatively characterized by the dispersion parameter α, in any noise conditions and corrections.

Spectral prior image constrained compressed sensing (spectral PICCS) for photon-counting computed tomography

Photon-counting computed tomography (PCCT) is an emerging imaging technique that enables multi-energy imaging with only a single scan acquisition. To enable multi-energy imaging, the detected photons corresponding to the full x-ray spectrum are divided into several subgroups of bin data that correspond to narrower energy windows. Consequently, noise in each energy bin increases compared to the full-spectrum data. This work proposes an iterative reconstruction algorithm for noise suppression in the narrower energy bins used in PCCT imaging. The algorithm is based on the framework of prior image constrained compressed sensing (PICCS) and is called spectral PICCS; it uses the full-spectrum image reconstructed using conventional filtered back-projection as the prior image. The spectral PICCS algorithm is implemented using a constrained optimization scheme with adaptive iterative step sizes such that only two tuning parameters are required in most cases. The algorithm was first evaluated using computer simulations, and then validated by both physical phantoms and in vivo swine studies using a research PCCT system. Results from both computer-simulation and experimental studies showed substantial image noise reduction in narrow energy bins (43-73%) without sacrificing CT number accuracy or spatial resolution.

Combination of voxel-based and projection-based methods in terms of convergence for CT reconstruction

PURPOSE

Recent applications of iterative image reconstruction algorithms to multislice helical CT have shown that iterative reconstruction can significantly improve image quality and reduce artifacts. In this paper, the authors introduce a combination of two different algorithms with different convergence properties: ordered subsets separable paraboloidal surrogates (OS-SPS) and iterative coordinate descent (ICD). The first one updates image voxels simultaneously, slightly changing attenuation values iteration by iteration. The second algorithm updates image voxel by voxel, each time performing full forward and backward projections of the voxel. It has been shown that ICD converges better at high-frequency areas and requires more iterations to reconstruct low-frequency components of the image. In contrast to ICD, SPS requires multiple iterations to reconstruct high-frequency areas. In this paper, the authors introduce an algorithm which leverages the benefits of both ICD and SPS.

METHODS

The idea is to update the entire image with SPS, determine high-frequency components, and focus ICD computations on it using nonhomogeneous ICD update.

RESULTS

The authors have successfully implemented OS-SPS, ICD, their hybrid approach, and few variations of ICD based on spatially nonuniform updates.

CONCLUSIONS

The authors have examined the convergence of different algorithms and found that proposed algorithm converges better than OS-SPS, ICD, as well as various improved variants of ICD.

Accelerated statistical reconstruction for C-arm cone-beam CT using Nesterov's method

PURPOSE

To accelerate model-based iterative reconstruction (IR) methods for C-arm cone-beam CT (CBCT), thereby combining the benefits of improved image quality and/or reduced radiation dose with reconstruction times on the order of minutes rather than hours.

METHODS

The ordered-subsets, separable quadratic surrogates (OS-SQS) algorithm for solving the penalized-likelihood (PL) objective was modified to include Nesterov's method, which utilizes "momentum" from image updates of previous iterations to better inform the current iteration and provide significantly faster convergence. Reconstruction performance of an anthropomorphic head phantom was assessed on a benchtop CBCT system, followed by CBCT on a mobile C-arm, which provided typical levels of incomplete data, including lateral truncation. Additionally, a cadaveric torso that presented realistic soft-tissue and bony anatomy was imaged on the C-arm, and different projectors were assessed for reconstruction speed.

RESULTS

Nesterov's method provided equivalent image quality to OS-SQS while reducing the reconstruction time by an order of magnitude (10.0 ×) by reducing the number of iterations required for convergence. The faster projectors were shown to produce similar levels of convergence as more accurate projectors and reduced the reconstruction time by another 5.3 ×. Despite the slower convergence of IR with truncated C-arm CBCT, comparison of PL reconstruction methods implemented on graphics processing units showed that reconstruction time was reduced from 106 min for the conventional OS-SQS method to as little as 2.0 min with Nesterov's method for a volumetric reconstruction of the head. In body imaging, reconstruction of the larger cadaveric torso was reduced from 159 min down to 3.3 min with Nesterov's method.

CONCLUSIONS

The acceleration achieved through Nesterov's method combined with ordered subsets reduced IR times down to a few minutes. This improved compatibility with clinical workflow better enables broader adoption of IR in CBCT-guided procedures, with corresponding benefits in overcoming conventional limits of image quality at lower dose.

A perceptual map for gait symmetry quantification and pathology detection

BACKGROUND

The gait movement is an essential process of the human activity and the result of collaborative interactions between the neurological, articular and musculoskeletal systems, working efficiently together. This explains why gait analysis is important and increasingly used nowadays for the diagnosis of many different types (neurological, muscular, orthopedic, etc.) of diseases. This paper introduces a novel method to quickly visualize the different parts of the body related to an asymmetric movement in the human gait of a patient for daily clinical usage. The proposed gait analysis algorithm relies on the fact that the healthy walk has (temporally shift-invariant) symmetry properties in the coronal plane. The goal is to provide an inexpensive and easy-to-use method, exploiting an affordable consumer depth sensor, the Kinect, to measure the gait asymmetry and display results in a perceptual way.

METHOD

We propose a multi-dimensional scaling mapping using a temporally shift invariant distance, allowing us to efficiently visualize (in terms of perceptual color difference) the asymmetric body parts of the gait cycle of a subject. We also propose an index computed from this map and which quantifies locally and globally the degree of asymmetry.

RESULTS

The proposed index is proved to be statistically significant and this new, inexpensive, marker-less, non-invasive, easy to set up, gait analysis system offers a readable and flexible tool for clinicians to analyze gait characteristics and to provide a fast diagnostic.

CONCLUSION

This system, which estimates a perceptual color map providing a quick overview of asymmetry existing in the gait cycle of a subject, can be easily exploited for disease progression, recovery cues from post-operative surgery (e.g., to check the healing process or the effect of a treatment or a prosthesis) or might be used for other pathologies where gait asymmetry might be a symptom.

Bayesian approach to time-resolved tomography

Conventional X-ray micro-computed tomography (μCT) is unable to meet the need for real-time, high-resolution, time-resolved imaging of multi-phase fluid flow. High signal-to-noise-ratio (SNR) data acquisition is too slow and results in motion artefacts in the images, while fast acquisition is too noisy and results in poor image contrast. We present a Bayesian framework for time-resolved tomography that uses priors to drastically reduce the required amount of experiment data. This enables high-quality time-resolved imaging through a data acquisition protocol that is both rapid and high SNR. Here we show that the framework: (i) encompasses our previous, algorithms for imaging two-phase flow as limiting cases; (ii) produces more accurate results from imperfect (i.e. real) data, where it can be compared to our previous work; and (iii) is generalisable to previously intractable systems, such as three-phase flow.

Dictionary learning for data recovery in positron emission tomography

Compressed sensing (CS) aims to recover images from fewer measurements than that governed by the Nyquist sampling theorem. Most CS methods use analytical predefined sparsifying domains such as total variation, wavelets, curvelets, and finite transforms to perform this task. In this study, we evaluated the use of dictionary learning (DL) as a sparsifying domain to reconstruct PET images from partially sampled data, and compared the results to the partially and fully sampled image (baseline).A CS model based on learning an adaptive dictionary over image patches was developed to recover missing observations in PET data acquisition. The recovery was done iteratively in two steps: a dictionary learning step and an image reconstruction step. Two experiments were performed to evaluate the proposed CS recovery algorithm: an IEC phantom study and five patient studies. In each case, 11% of the detectors of a GE PET/CT system were removed and the acquired sinogram data were recovered using the proposed DL algorithm. The recovered images (DL) as well as the partially sampled images (with detector gaps) for both experiments were then compared to the baseline. Comparisons were done by calculating RMSE, contrast recovery and SNR in ROIs drawn in the background, and spheres of the phantom as well as patient lesions.For the phantom experiment, the RMSE for the DL recovered images were 5.8% when compared with the baseline images while it was 17.5% for the partially sampled images. In the patients' studies, RMSE for the DL recovered images were 3.8%, while it was 11.3% for the partially sampled images. Our proposed CS with DL is a good approach to recover partially sampled PET data. This approach has implications toward reducing scanner cost while maintaining accurate PET image quantification.

The Three-Dimensional Morphology of Growing Dendrites

The processes controlling the morphology of dendrites have been of great interest to a wide range of communities, since they are examples of an out-of-equilibrium pattern forming system, there is a clear connection with battery failure processes, and their morphology sets the properties of many metallic alloys. We determine the three-dimensional morphology of free growing metallic dendrites using a novel X-ray tomographic technique that improves the temporal resolution by more than an order of magnitude compared to conventional techniques. These measurements show that the growth morphology of metallic dendrites is surprisingly different from that seen in model systems, the morphology is not self-similar with distance back from the tip, and that this morphology can have an unexpectedly strong influence on solute segregation in castings. These experiments also provide benchmark data that can be used to validate simulations of free dendritic growth.

Strain in a silicon-on-insulator nanostructure revealed by 3D x-ray Bragg ptychography

Progresses in the design of well-defined electronic band structure and dedicated functionalities rely on the high control of complex architectural device nano-scaled structures. This includes the challenging accurate description of strain fields in crystalline structures, which requires non invasive and three-dimensional (3D) imaging methods. Here, we demonstrate in details how x-ray Bragg ptychography can be used to quantify in 3D a displacement field in a lithographically patterned silicon-on-insulator structure. The image of the crystalline properties, which results from the phase retrieval of a coherent intensity data set, is obtained from a well-controlled optimized process, for which all steps are detailed. These results confirm the promising perspectives of 3D Bragg ptychography for the investigation of complex nano-structured crystals in material science.

Edge-preserving PET image reconstruction using trust optimization transfer

Iterative image reconstruction for positron emission tomography can improve image quality by using spatial regularization. The most commonly used quadratic penalty often oversmoothes sharp edges and fine features in reconstructed images, while nonquadratic penalties can preserve edges and achieve higher contrast recovery. Existing optimization algorithms such as the expectation maximization (EM) and preconditioned conjugate gradient (PCG) algorithms work well for the quadratic penalty, but are less efficient for high-curvature or nonsmooth edge-preserving regularizations. This paper proposes a new algorithm to accelerate edge-preserving image reconstruction by using two strategies: trust surrogate and optimization transfer descent. Trust surrogate approximates the original penalty by a smoother function at each iteration, but guarantees the algorithm to descend monotonically; Optimization transfer descent accelerates a conventional optimization transfer algorithm by using conjugate gradient and line search. Results of computer simulations and real 3-D data show that the proposed algorithm converges much faster than the conventional EM and PCG for smooth edge-preserving regularization and can also be more efficient than the current state-of-art algorithms for the nonsmooth l1 regularization.

Low dose dynamic CT myocardial perfusion imaging using a statistical iterative reconstruction method

PURPOSE

Dynamic CT myocardial perfusion imaging has the potential to provide both functional and anatomical information regarding coronary artery stenosis. However, radiation dose can be potentially high due to repeated scanning of the same region. The purpose of this study is to investigate the use of statistical iterative reconstruction to improve parametric maps of myocardial perfusion derived from a low tube current dynamic CT acquisition.

METHODS

Four pigs underwent high (500 mA) and low (25 mA) dose dynamic CT myocardial perfusion scans with and without coronary occlusion. To delineate the affected myocardial territory, an N-13 ammonia PET perfusion scan was performed for each animal in each occlusion state. Filtered backprojection (FBP) reconstruction was first applied to all CT data sets. Then, a statistical iterative reconstruction (SIR) method was applied to data sets acquired at low dose. Image voxel noise was matched between the low dose SIR and high dose FBP reconstructions. CT perfusion maps were compared among the low dose FBP, low dose SIR and high dose FBP reconstructions. Numerical simulations of a dynamic CT scan at high and low dose (20:1 ratio) were performed to quantitatively evaluate SIR and FBP performance in terms of flow map accuracy, precision, dose efficiency, and spatial resolution.

RESULTS

Forin vivo studies, the 500 mA FBP maps gave -88.4%, -96.0%, -76.7%, and -65.8% flow change in the occluded anterior region compared to the open-coronary scans (four animals). The percent changes in the 25 mA SIR maps were in good agreement, measuring -94.7%, -81.6%, -84.0%, and -72.2%. The 25 mA FBP maps gave unreliable flow measurements due to streaks caused by photon starvation (percent changes of +137.4%, +71.0%, -11.8%, and -3.5%). Agreement between 25 mA SIR and 500 mA FBP global flow was -9.7%, 8.8%, -3.1%, and 26.4%. The average variability of flow measurements in a nonoccluded region was 16.3%, 24.1%, and 937.9% for the 500 mA FBP, 25 mA SIR, and 25 mA FBP, respectively. In numerical simulations, SIR mitigated streak artifacts in the low dose data and yielded flow maps with mean error <7% and standard deviation <9% of mean, for 30 × 30 pixel ROIs (12.9 × 12.9 mm(2)). In comparison, low dose FBP flow errors were -38% to +258%, and standard deviation was 6%-93%. Additionally, low dose SIR achieved 4.6 times improvement in flow map CNR(2) per unit input dose compared to low dose FBP.

CONCLUSIONS

SIR reconstruction can reduce image noise and mitigate streaking artifacts caused by photon starvation in dynamic CT myocardial perfusion data sets acquired at low dose (low tube current), and improve perfusion map quality in comparison to FBP reconstruction at the same dose.