Globally convergent algorithms for maximum a posteriori transmission tomography

A Majorization-Minimization Algorithm for Neuroimage Registration

Intensity-based image registration is critical for neuroimaging tasks, such as 3D reconstruction, times-series alignment, and common coordinate mapping. The gradient-based optimization methods commonly used to solve this problem require a careful selection of step-length. This limitation imposes substantial time and computational costs. Here we propose a gradient-independent rigid-motion registration algorithm based on the majorization-minimization (MM) principle. Each iteration of our intensity-based MM algorithm reduces to a simple point-set rigid registration problem with a closed form solution that avoids the step-length issue altogether. The details of the algorithm are presented, and an error bound for its more practical truncated form is derived. The performance of the MM algorithm is shown to be more effective than gradient descent on simulated images and Nissl stained coronal slices of mouse brain. We also compare and contrast the similarities and differences between the MM algorithm and another gradient-free registration algorithm called the block-matching method. Finally, extensions of this algorithm to more complex problems are discussed.

Model-based deep CNN-regularized reconstruction for digital breast tomosynthesis with a task-based CNN image assessment approach

Objective. Digital breast tomosynthesis (DBT) is a quasi-three-dimensional breast imaging modality that improves breast cancer screening and diagnosis because it reduces fibroglandular tissue overlap compared with 2D mammography. However, DBT suffers from noise and blur problems that can lower the detectability of subtle signs of cancers such as microcalcifications (MCs). Our goal is to improve the image quality of DBT in terms of image noise and MC conspicuity.Approach. We proposed a model-based deep convolutional neural network (deep CNN or DCNN) regularized reconstruction (MDR) for DBT. It combined a model-based iterative reconstruction (MBIR) method that models the detector blur and correlated noise of the DBT system and the learning-based DCNN denoiser using the regularization-by-denoising framework. To facilitate the task-based image quality assessment, we also proposed two DCNN tools for image evaluation: a noise estimator (CNN-NE) trained to estimate the root-mean-square (RMS) noise of the images, and an MC classifier (CNN-MC) as a DCNN model observer to evaluate the detectability of clustered MCs in human subject DBTs.Main results. We demonstrated the efficacies of CNN-NE and CNN-MC on a set of physical phantom DBTs. The MDR method achieved low RMS noise and the highest detection area under the receiver operating characteristic curve (AUC) rankings evaluated by CNN-NE and CNN-MC among the reconstruction methods studied on an independent test set of human subject DBTs.Significance. The CNN-NE and CNN-MC may serve as a cost-effective surrogate for human observers to provide task-specific metrics for image quality comparisons. The proposed reconstruction method shows the promise of combining physics-based MBIR and learning-based DCNNs for DBT image reconstruction, which may potentially lead to lower dose and higher sensitivity and specificity for MC detection in breast cancer screening and diagnosis.

Kernel graph filtering-A new method for dynamic sinogram denoising

Low count PET (positron emission tomography) imaging is often desirable in clinical diagnosis and biomedical research, but its images are generally very noisy, due to the very weak signals in the sinograms used in image reconstruction. To address this issue, this paper presents a novel kernel graph filtering method for dynamic PET sinogram denoising. This method is derived from treating the dynamic sinograms as the signals on a graph, and learning the graph adaptively from the kernel principal components of the sinograms to construct a lowpass kernel graph spectrum filter. The kernel graph filter thus obtained is then used to filter the original sinogram time frames to obtain the denoised sinograms for PET image reconstruction. Extensive tests and comparisons on the simulated and real life in-vivo dynamic PET datasets show that the proposed method outperforms the existing methods in sinogram denoising and image enhancement of dynamic PET at all count levels, especially at low count, with a great potential in real life applications of dynamic PET imaging.

Improvement in sampling and modulation of multiplexing with temporal shuttering of adaptable apertures in a brain-dedicated multi-pinhole SPECT system

We are developing a multi-detector pinhole-based stationary brain-dedicated SPECT system: AdaptiSPECT-C. In this work, we introduced a new design prototype with multiple adaptable pinhole apertures for each detector to modulate the multiplexing by employing temporal shuttering of apertures. Temporal shuttering of apertures over the scan time provides the AdaptiSPECT-C with the capability of multiple-frame acquisition. We investigated, through analytic simulation, the impact of projection multiplexing on image quality using several digital phantoms and a customized anthropomorphic phantom emulating brain perfusion clinical distribution. The 105 pinholes in the collimator of the system were categorized into central, axial, and lateral apertures. We generated, through simulation, collimators of different multiplexing levels. Several data acquisition schemes were also created by changing the imaging time share of the acquisition frames. Sensitivity increased by 35% compared to the single-pinhole-per-detector base configuration of the AdaptiSPECT-C when using the central, axial, and lateral apertures with equal acquisition time shares within a triple-frame scheme with a high multiplexing scenario. Axial and angular sampling of the base configuration was enhanced by adding the axial and lateral apertures. We showed that the temporal shuttering of apertures can be exploited, trading the sensitivity, to modulate the multiplexing and to acquire a set of non-multiplexed non-truncated projections. Our results suggested that reconstruction benefited from utilizing both non-multiplexed projections and projections with modulated multiplexing resulting in a noticeably reduction in the multiplexing-induced image artefacts. Contrast recovery factor improved by 20% (9%) compared to the base configuration for a Defrise (hot-rod) phantom study when the central and axial (lateral) apertures with equal time shares were combined. The results revealed that, as an overall trend at each simulated multiplexing level, lowest normalized root-mean-square errors for the brain gray-matter regions were achieved with the combined usage of the central apertures and axial/lateral apertures.

Investigation of Axial and Angular Sampling in Multi-Detector Pinhole-SPECT Brain Imaging

We designed a dedicated multi-detector multi-pinhole brain SPECT scanner to generate images of higher quality compared to general-purpose systems. The system, AdaptiSPECT-C, is intended to adapt its sensitivity-resolution trade-off by varying its aperture configurations allowing both high-sensitivity dynamic and high-spatial-resolution static imaging. The current system design consists of 23 detector heads arranged in a truncated spherical geometry. In this work, we investigated the axial and angular sampling capability of the current stationary system design. Two data acquisition schemes using limited rotation of the gantry and two others using axial translation of the imaging bed were also evaluated concerning their impact on image quality through improved sampling. Increasing both angular and axial sampling in the current prototype system resulted in quantitative improvements in image quality metrics and qualitative appearance of the images as determined in studies with specifically selected phantoms. Visual improvements for the brain phantoms with clinical distributions were less pronounced but presented quantitative improvements in the fidelity (normalized root-mean-square error (NRMSE)) and striatal specific binding ratio (SBR) for a dopamine transporter (DAT) distribution, and in NRMSE and activity recovery for a brain perfusion distribution. More pronounced improvements with increased sampling were seen in contrast recovery coefficient, bias, and coefficient of variation for a lesion in the brain perfusion distribution. The negligible impact of the most cranial ring of detectors on axial sampling, but its significant impact on sensitivity and angular sampling in the cranial portion of the imaging volume-of-interest were also determined.

Digital Breast Tomosynthesis: Technique and Common Artifacts

Image optimization at digital breast tomosynthesis (DBT) involves a series of trade-offs between multiple variables. Wider sweep angles provide better separation of overlapping tissues, but they result in decreased in-plane resolution as well as increased scan times that may be prone to patient motion. Techniques to reduce scan time, such as continuous tube motion and pixel binning during detector readout, reduce the chances of patient motion but may degrade the in-plane resolution. Image artifacts are inherent to DBT because of the limited angular range of the acquisition. Iterative reconstruction algorithms have been shown to reduce various DBT 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.

Fast Statistical Iterative Reconstruction for Mega-voltage Computed Tomography

Statistical iterative reconstruction is expected to improve the image quality of computed tomography (CT). However, one of the challenges of iterative reconstruction is its large computational cost. The purpose of this review is to summarize a fast iterative reconstruction algorithm by optimizing reconstruction parameters. Megavolt projection data was acquired from a TomoTherapy system and reconstructed using in-house statistical iterative reconstruction algorithm. Total variation was used as the regularization term and the weight of the regularization term was determined by evaluating signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), and visual assessment of spatial resolution using Gammex and Cheese phantoms. Gradient decent with an adaptive convergence parameter, ordered subset expectation maximization (OSEM), and CPU/GPU parallelization were applied in order to accelerate the present reconstruction algorithm. The SNR and CNR of the iterative reconstruction were several times better than that of filtered back projection (FBP). The GPU parallelization code combined with the OSEM algorithm reconstructed an image several hundred times faster than a CPU calculation. With 500 iterations, which provided good convergence, our method produced a 512 × 512 pixel image within a few seconds. The image quality of the present algorithm was much better than that of FBP for patient data. J. Med. Invest. 67 : 30-39, February, 2020.

Svahn T. Evaluation of a new image reconstruction method for digital breast tomosynthesis: effects on the visibility of breast lesions and breast density

OBJECTIVE

To compare image quality and breast density of two reconstruction methods, the widely-used filtered-back projection (FBP) reconstruction and the iterative heuristic Bayesian inference reconstruction (Bayesian inference reconstruction plus the method of total variation applied, HBI).

METHODS

Thirty-two clinical DBT data sets with malignant and benign findings, n = 27 and 17, respectively, were reconstructed using FBP and HBI. Three experienced radiologists evaluated the images independently using a 5-point visual grading scale and classified breast density according to the American College of Radiology Breast Imaging-Reporting And Data System Atlas, fifth edition. Image quality metrics included lesion conspicuity, clarity of lesion borders and spicules, noise level, artifacts surrounding the lesion, visibility of parenchyma and breast density.

RESULTS

For masses, the image quality of HBI reconstructions was superior to that of FBP in terms of conspicuity,clarity of lesion borders and spicules (p < 0.01). HBI and FBP were not significantly different in calcification conspicuity. Overall, HBI reduced noise and supressed artifacts surrounding the lesions better (p < 0.01). The visibility of fibroglandular parenchyma increased using the HBI method (p < 0.01). On average, five cases per radiologist were downgraded from BI-RADS breast density category C/D to A/B.

CONCLUSION

HBI significantly improves lesion visibility compared to FBP. HBI-visibility of breast parenchyma increased, leading to a lower breast density rating. Applying the HBIR algorithm should improve the diagnostic performance of DBT and decrease the need for additional imaging in patients with dense breasts.

ADVANCES IN KNOWLEDGE

Iterative heuristic Bayesian inference (HBI) image reconstruction substantially improves the image quality of breast tomosynthesis leading to a better visibility of breast carcinomas and reduction of the perceived breast density compared to the widely-used filtered-back projection (FPB) reconstruction. Applying HBI should improve the accuracy of breast tomosynthesis and reduce the number of unnecessary breast biopsies. It may also reduce the radiation dose for the patients, which is especially important in the screening context.

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.

Technical Note: Emission expectation maximization look-alike algorithms for x-ray CT and other applications

PURPOSE

In emission tomography, the expectation maximization (EM) algorithm is easy to use with only one parameter to adjust - the number of iterations. On the other hand, the EM algorithms for transmission tomography are not so user-friendly and have many problems. This paper develops a new transmission algorithm similar to the emission EM algorithm.

METHODS

This paper develops a family of emission-EM-look-alike algorithms by expressing the emission EM algorithm in the additive form and changing the weighting factor. One of the family members can be applied to transmission tomography such as the x-ray computed tomography (CT).

RESULTS

Computer simulations are performed and compared with a similar algorithm by a different group using the transmission CT noise model. Our algorithm has the same convergence rate as theirs, and our algorithm provides better contrast-to-noise ratio for lesion detection.

CONCLUSIONS

For any noise variance function, an emission-EM-look-alike algorithm can be derived. This algorithm preserves many properties of the emission EM algorithm such as multiplicative update, non-negativity, faster convergence rate for the bright objects, and ease of implementation.

Detector Blur and Correlated Noise Modeling for Digital Breast Tomosynthesis Reconstruction

This paper describes a new image reconstruction method for digital breast tomosynthesis (DBT). The new method incorporates detector blur into the forward model. The detector blur in DBT causes correlation in the measurement noise. By making a few approximations that are reasonable for breast imaging, we formulated a regularized quadratic optimization problem with a data-fit term that incorporates models for detector blur and correlated noise (DBCN). We derived a computationally efficient separable quadratic surrogate (SQS) algorithm to solve the optimization problem that has a non-diagonal noise covariance matrix. We evaluated the SQS-DBCN method by reconstructing DBT scans of breast phantoms and human subjects. The contrast-to-noise ratio and sharpness of microcalcifications were analyzed and compared with those by the simultaneous algebraic reconstruction technique. The quality of soft tissue lesions and parenchymal patterns was examined. The results demonstrate the potential to improve the image quality of reconstructed DBT images by incorporating the system physics model. This paper is a first step toward model-based iterative reconstruction for DBT.

A fast 4D cone beam CT reconstruction method based on the OSC-TV algorithm

BACKGROUND

Four-dimensional cone beam computed tomography allows for temporally resolved imaging with useful applications in radiotherapy, but raises particular challenges in terms of image quality and computation time.

OBJECTIVE

The purpose of this work is to develop a fast and accurate 4D algorithm by adapting a GPU-accelerated ordered subsets convex algorithm (OSC), combined with the total variation minimization regularization technique (TV).

METHODS

Different initialization schemes were studied to adapt the OSC-TV algorithm to 4D reconstruction: each respiratory phase was initialized either with a 3D reconstruction or a blank image. Reconstruction algorithms were tested on a dynamic numerical phantom and on a clinical dataset. 4D iterations were implemented for a cluster of 8 GPUs.

RESULTS

All developed methods allowed for an adequate visualization of the respiratory movement and compared favorably to the McKinnon-Bates and adaptive steepest descent projection onto convex sets algorithms, while the 4D reconstructions initialized from a prior 3D reconstruction led to better overall image quality.

CONCLUSION

The most suitable adaptation of OSC-TV to 4D CBCT was found to be a combination of a prior FDK reconstruction and a 4D OSC-TV reconstruction with a reconstruction time of 4.5 minutes. This relatively short reconstruction time could facilitate a clinical use.

Cone-beam CT reconstruction for non-periodic organ motion using time-ordered chain graph model

Purpose

The purpose of this study is to introduce the new concept of a four-dimensional (4D) cone-beam computed tomography (CBCT) reconstruction approach for non-periodic organ motion in cooperation with the time-ordered chain graph model (TCGM) and to compare it with previously developed methods such as total variation-based compressed sensing (TVCS) and prior-image constrained compressed sensing (PICCS).

Materials and Methods

Our proposed reconstruction is based on a model including the constraint originating from the images of neighboring time phases. Namely, the reconstructed time-series images depend on each other in this TCGM scheme, and the time-ordered images are concurrently reconstructed in the iterative reconstruction approach. In this study, iterative reconstruction with the TCGM was carried out with 90° projection ranges. The images reconstructed by the TCGM were compared with the images reconstructed by TVCS (200° projection ranges) and PICCS (90° projection ranges).

Two kinds of projection data sets–an elliptic-cylindrical digital phantom and two clinical patients’ data–were used. For the digital phantom, an air sphere was contained and virtually moved along the longitudinal axis by 3 cm/30 s and 3 cm/60 s; the temporal resolution was evaluated by measuring the penumbral width of the air sphere. The clinical feasibility of the non-periodic time-ordered 4D CBCT image reconstruction was examined with the patient data in the pelvic region.

Results

In the evaluation of the digital-phantom reconstruction, the penumbral widths of the TCGM yielded the narrowest result; the results obtained by PICCS and TCGM using 90° projection ranges were 2.8% and 18.2% for 3 cm/30 s, and 5.0% and 23.1% for 3 cm/60 s narrower than that of TVCS using 200° projection ranges. This suggests that the TCGM has a better temporal resolution, whereas PICCS seems similar to TVCS. These reconstruction methods were also compared using patients’ projection data sets. Although all three reconstruction results showed motion related to rectal gas or stool, the result obtained by the TCGM was visibly clearer with less blurring.

Conclusion

The TCGM is a feasible approach to visualize non-periodic organ motion. The digital-phantom results demonstrated that the proposed method provides 4D image series with a better temporal resolution compared to TVCS and PICCS. The clinical patients’ results also showed that the present method enables us to visualize motion related to rectal gas and flatus in the rectum.

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.

Development and Evaluation of Image Reconstruction Algorithms for a Novel Desktop SPECT System

OBJECTIVE S

Various iterative reconstruction algorithms in nuclear medicine have been introduced in the last three decades. For each new imaging system, it is wise to select appropriate image reconstruction algorithms and evaluate their performance. In this study, three approaches of image reconstruction were developed for a novel desktop open-gantry SPECT system, PERSPECT, to assess their performance in terms of the quality of the resultant reconstructed images.

METHODS

In the present work, a proposed image reconstruction algorithm for the PERSPECT, referred to as quasi-simultaneous multiplicative algebraic reconstruction technique (qSMART), together with two popular image reconstruction methods, maximum-likelihood expectation-maximization (MLEM) and ordered-subsets EM (OSEM), were implemented and compared. Analytic and Monte Carlo simulations were applied for data acquisition of various phantoms including a micro-Derenzo phantom. All acquired data were reconstructed by the three algorithms using different number of iterations (1-40 ). A thorough set of figures-of-merit was utilized to quantitatively compare the generated images.

RESULTS

OSEM depicted reconstructed images of higher (or matching) quality in comparison to qSMART. MLEM also reached nearly similar quality as OSEM but at higher number of iterations. The graph of data discrepancy revealed that the ranking of the three approaches in terms of convergence speed is as qSMART, OSEM, and MLEM. Furthermore, bias-versus-noise curves indicated that optimal bias-noise results were achieved using OSEM.

CONCLUSION

The results showed that although qSMART can be applied for image reconstruction if being halted in the early iterations (up to 5), the best achievable quality of images is obtained using the OSEM.

Optimized MLAA for quantitative non-TOF PET/MR of the brain

For quantitative tracer distribution in positron emission tomography, attenuation correction is essential. In a hybrid PET/CT system the CT images serve as a basis for generation of the attenuation map, but in PET/MR, the MR images do not have a similarly simple relationship with the attenuation map. Hence attenuation correction in PET/MR systems is more challenging. Typically either of two MR sequences are used: the Dixon or the ultra-short time echo (UTE) techniques. However these sequences have some well-known limitations. In this study, a reconstruction technique based on a modified and optimized non-TOF MLAA is proposed for PET/MR brain imaging. The idea is to tune the parameters of the MLTR applying some information from an attenuation image computed from the UTE sequences and a T1w MR image. In this MLTR algorithm, an [Formula: see text] parameter is introduced and optimized in order to drive the algorithm to a final attenuation map most consistent with the emission data. Because the non-TOF MLAA is used, a technique to reduce the cross-talk effect is proposed. In this study, the proposed algorithm is compared to the common reconstruction methods such as OSEM using a CT attenuation map, considered as the reference, and OSEM using the Dixon and UTE attenuation maps. To show the robustness and the reproducibility of the proposed algorithm, a set of 204 [¹⁸F]FDG patients, 35 [¹¹C]PiB patients and 1 [¹⁸F]FET patient are used. The results show that by choosing an optimized value of [Formula: see text] in MLTR, the proposed algorithm improves the results compared to the standard MR-based attenuation correction methods (i.e. OSEM using the Dixon or the UTE attenuation maps), and the cross-talk and the scale problem are limited.

Statistical iterative reconstruction to improve image quality for digital breast tomosynthesis

PURPOSE

Digital breast tomosynthesis (DBT) is a novel modality with the potential to improve early detection of breast cancer by providing three-dimensional (3D) imaging with a low radiation dose. 3D image reconstruction presents some challenges: cone-beam and flat-panel geometry, and highly incomplete sampling. A promising means of overcome these challenges is statistical iterative reconstruction (IR), since it provides the flexibility of accurate physics modeling and a general description of system geometry. The authors' goal was to develop techniques for applying statistical IR to tomosynthesis imaging data.

METHODS

These techniques include the following: a physics model with a local voxel-pair based prior with flexible parameters to fine-tune image quality; a precomputed parameter λ in the prior, to remove data dependence and to achieve a uniform resolution property; an effective ray-driven technique to compute the forward and backprojection; and an oversampled, ray-driven method to perform high resolution reconstruction with a practical region-of-interest technique. To assess the performance of these techniques, the authors acquired phantom data on the stationary DBT prototype system. To solve the estimation problem, the authors proposed an optimization-transfer based algorithm framework that potentially allows fewer iterations to achieve an acceptably converged reconstruction.

RESULTS

IR improved the detectability of low-contrast and small microcalcifications, reduced cross-plane artifacts, improved spatial resolution, and lowered noise in reconstructed images.

CONCLUSIONS

Although the computational load remains a significant challenge for practical development, the superior image quality provided by statistical IR, combined with advancing computational techniques, may bring benefits to screening, diagnostics, and intraoperative imaging in clinical applications.

Accelerating an Ordered-Subset Low-Dose X-Ray Cone Beam Computed Tomography Image Reconstruction with a Power Factor and Total Variation Minimization

In recent years, there has been increased interest in low-dose X-ray cone beam computed tomography (CBCT) in many fields, including dentistry, guided radiotherapy and small animal imaging. Despite reducing the radiation dose, low-dose CBCT has not gained widespread acceptance in routine clinical practice. In addition to performing more evaluation studies, developing a fast and high-quality reconstruction algorithm is required. In this work, we propose an iterative reconstruction method that accelerates ordered-subsets (OS) reconstruction using a power factor. Furthermore, we combine it with the total-variation (TV) minimization method. Both simulation and phantom studies were conducted to evaluate the performance of the proposed method. Results show that the proposed method can accelerate conventional OS methods, greatly increase the convergence speed in early iterations. Moreover, applying the TV minimization to the power acceleration scheme can further improve the image quality while preserving the fast convergence rate.

Object Specific Trajectory Optimization for Industrial X-ray Computed Tomography

In industrial settings, X-ray computed tomography scans are a common tool for inspection of objects. Often the object can not be imaged using standard circular or helical trajectories because of constraints in space or time. Compared to medical applications the variance in size and materials is much larger. Adapting the acquisition trajectory to the object is beneficial and sometimes inevitable. There are currently no sophisticated methods for this adoption. Typically the operator places the object according to his best knowledge. We propose a detectability index based optimization algorithm which determines the scan trajectory on the basis of a CAD-model of the object. The detectability index is computed solely from simulated projections for multiple user defined features. By adapting the features the algorithm is adapted to different imaging tasks. Performance of simulated and measured data was qualitatively and quantitatively assessed.The results illustrate that our algorithm not only allows more accurate detection of features, but also delivers images with high overall quality in comparison to standard trajectory reconstructions. This work enables to reduce the number of projections and in consequence scan time by introducing an optimization algorithm to compose an object specific trajectory.

GPU-accelerated regularized iterative reconstruction for few-view cone beam CT

PURPOSE

The present work proposes an iterative reconstruction technique designed for x-ray transmission computed tomography (CT). The main objective is to provide a model-based solution to the cone-beam CT reconstruction problem, yielding accurate low-dose images via few-views acquisitions in clinically acceptable time frames.

METHODS

The proposed technique combines a modified ordered subsets convex (OSC) algorithm and the total variation minimization (TV) regularization technique and is called OSC-TV. The number of subsets of each OSC iteration follows a reduction pattern in order to ensure the best performance of the regularization method. Considering the high computational cost of the algorithm, it is implemented on a graphics processing unit, using parallelization to accelerate computations.

RESULTS

The reconstructions were performed on computer-simulated as well as human pelvic cone-beam CT projection data and image quality was assessed. In terms of convergence and image quality, OSC-TV performs well in reconstruction of low-dose cone-beam CT data obtained via a few-view acquisition protocol. It compares favorably to the few-view TV-regularized projections onto convex sets (POCS-TV) algorithm. It also appears to be a viable alternative to full-dataset filtered backprojection. Execution times are of 1-2 min and are compatible with the typical clinical workflow for nonreal-time applications.

CONCLUSIONS

Considering the image quality and execution times, this method may be useful for reconstruction of low-dose clinical acquisitions. It may be of particular benefit to patients who undergo multiple acquisitions by reducing the overall imaging radiation dose and associated risks.

Methods for clinical evaluation of noise reduction techniques in abdominopelvic CT

Most noise reduction methods involve nonlinear processes, and objective evaluation of image quality can be challenging, since image noise cannot be fully characterized on the sole basis of the noise level at computed tomography (CT). Noise spatial correlation (or noise texture) is closely related to the detection and characterization of low-contrast objects and may be quantified by analyzing the noise power spectrum. High-contrast spatial resolution can be measured using the modulation transfer function and section sensitivity profile and is generally unaffected by noise reduction. Detectability of low-contrast lesions can be evaluated subjectively at varying dose levels using phantoms containing low-contrast objects. Clinical applications with inherent high-contrast abnormalities (eg, CT for renal calculi, CT enterography) permit larger dose reductions with denoising techniques. In low-contrast tasks such as detection of metastases in solid organs, dose reduction is substantially more limited by loss of lesion conspicuity due to loss of low-contrast spatial resolution and coarsening of noise texture. Existing noise reduction strategies for dose reduction have a substantial impact on lowering the radiation dose at CT. To preserve the diagnostic benefit of CT examination, thoughtful utilization of these strategies must be based on the inherent lesion-to-background contrast and the anatomy of interest. The authors provide an overview of existing noise reduction strategies for low-dose abdominopelvic CT, including analytic reconstruction, image and projection space denoising, and iterative reconstruction; review qualitative and quantitative tools for evaluating these strategies; and discuss the strengths and limitations of individual noise reduction methods.

Multigrid reconstruction with block-iterative updates for breast tomosynthesis

PURPOSE

The authors wish to evaluate the possible advantages of using a multigrid approach to maximum-a-posteriori reconstruction in digital breast tomosynthesis together with block-iterative updates in the form of either plane-by-plane updates or ordered subsets.

METHODS

The authors previously developed a penalized maximum likelihood reconstruction algorithm with resolution model dedicated to breast tomosynthesis [K. Michielsen et al., "Patchwork reconstruction with resolution modeling for digital breast tomosynthesis," Med. Phys. 40, 031105 (10pp.) (2013)]. This algorithm was extended with ordered subsets and multigrid updates, and the effects on the convergence and on limited angle artifact appearance were evaluated on a mathematical phantom and patient data. To ensure a fair comparison, the analysis was performed at the same computational cost for all methods. To assess convergence and artifact creation in the phantom reconstructions, the authors looked at posterior likelihood, sum of squared residuals, contrast of identical calcifications at different positions, and the standard deviation between the contrasts of these calcifications. For the patient cases, the authors calculated posterior likelihood, measured the signal difference to noise ratio of subtle microcalcifications, and visually evaluated the reconstructions.

RESULTS

The authors selected multigrid sequences scoring in the best 10% of the four evaluated parameters, except for the reconstructions with subsets where a low standard deviation of the contrast was incompatible with the three other parameters. In further evaluation of phantom reconstructions from noisy data and patient data, the authors found improved convergence and a reduction in artifacts for our chosen multigrid reconstructions compared to the single grid reconstructions with equivalent computational cost, although there was a diminishing return for an increasing number of subsets.

CONCLUSIONS

Multigrid reconstruction improves upon reconstruction with a fixed grid when evaluated at a fixed computational cost. For multigrid reconstruction, using plane-by-plane updates or applying ordered subsets resulted in similar performance.

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.

A Case for Wide-Angle Breast Tomosynthesis

RATIONALES AND OBJECTIVES

Conventional mammography is largely limited by superimposed anatomy. Digital breast tomosynthesis (DBT) and computed tomography (CT) alleviate this limitation but with added out-of-plane artifacts or limited chest wall coverage. This article presents a wide-angle breast tomosynthesis (WBT), aimed to provide a practical solution to these limitations, and offers an initial study of its utility in comparison with DBT and CT using a singular evaluation platform.

MATERIALS AND METHODS

Using an anthropomorphic virtual breast phantom, a Monte Carlo code modeled a breast imaging system for three modalities of DBT, WBT, and breast CT (44°, 99°, and 198° total angle range, respectively) at four breast compression levels, all at a constant mean glandular dose level of 1.5 mGy. Reconstructed volumes were generated using iterative reconstruction methods. Lesion detectability was estimated using contrast-to-noise ratio and a channelized Hotelling observer model in terms of the area under the receiver operating characteristic (AUC).

RESULTS

Results showed improved detection with increased angular span and compression. The estimated AUCs for WBT were similar to that of CT. Comparative performance averaged over all thicknesses between CT and WBT was 4.3 ± 3.0%, whereas that between WBT and DBT was 5.6 ± 1.0%. At compression levels reflective of the modality (7-, 5-, and 4-cm thickness for CT, WBT, and DBT, respectively), WBT yielded an AUC comparable to CT (performance difference of 1.2%) but superior to DBT (performance difference of 5.5%).

CONCLUSIONS

The proposed imaging modality showed significant advantages over conventional DBT. WBT exhibited superior imaging performance over DBT at lower compression levels, highlighting further potential for reduced breast compression.

Evaluation of time-efficient reconstruction methods in digital breast tomosynthesis

Three reconstruction algorithms for digital breast tomosynthesis were compared in this article: filtered back-projection (FBP), iterative adapted FBP and maximum likelihood-convex iterative algorithms. Quality metrics such as signal-difference-to-noise ratio, normalised line-profiles and artefact-spread function were used for evaluation of reconstructed tomosynthesis images. The iterative-based methods offered increased image quality in terms of higher detectability and reduced artefacts, which will be further examined in clinical images.

Evaluating the sensitivity of the optimization of acquisition geometry to the choice of reconstruction algorithm in digital breast tomosynthesis through a simulation study

Due to the limited number of views and limited angular span in digital breast tomosynthesis (DBT), the acquisition geometry design is an important factor that affects the image quality. Therefore, intensive studies have been conducted regarding the optimization of the acquisition geometry. However, different reconstruction algorithms were used in most of the reported studies. Because each type of reconstruction algorithm can provide images with its own image resolution, noise properties and artifact appearance, it is unclear whether the optimal geometries concluded for the DBT system in one study can be generalized to the DBT systems with a reconstruction algorithm different to the one applied in that study. Hence, we investigated the effect of the reconstruction algorithm on the optimization of acquisition geometry parameters through carefully designed simulation studies. Our results show that using various reconstruction algorithms, including the filtered back-projection, the simultaneous algebraic reconstruction technique, the maximum-likelihood method and the total-variation regularized least-square method, gave similar performance trends for the acquisition parameters for detecting lesions. The consistency of system ranking indicates that the choice of the reconstruction algorithm may not be critical for DBT system geometry optimization.

Statistical model based iterative reconstruction (MBIR) in clinical CT systems: experimental assessment of noise performance

PURPOSE

To reduce radiation dose in CT imaging, the statistical model based iterative reconstruction (MBIR) method has been introduced for clinical use. Based on the principle of MBIR and its nonlinear nature, the noise performance of MBIR is expected to be different from that of the well-understood filtered backprojection (FBP) reconstruction method. The purpose of this work is to experimentally assess the unique noise characteristics of MBIR using a state-of-the-art clinical CT system.

METHODS

Three physical phantoms, including a water cylinder and two pediatric head phantoms, were scanned in axial scanning mode using a 64-slice CT scanner (Discovery CT750 HD, GE Healthcare, Waukesha, WI) at seven different mAs levels (5, 12.5, 25, 50, 100, 200, 300). At each mAs level, each phantom was repeatedly scanned 50 times to generate an image ensemble for noise analysis. Both the FBP method with a standard kernel and the MBIR method (Veo(®), GE Healthcare, Waukesha, WI) were used for CT image reconstruction. Three-dimensional (3D) noise power spectrum (NPS), two-dimensional (2D) NPS, and zero-dimensional NPS (noise variance) were assessed both globally and locally. Noise magnitude, noise spatial correlation, noise spatial uniformity and their dose dependence were examined for the two reconstruction methods.

RESULTS

(1) At each dose level and at each frequency, the magnitude of the NPS of MBIR was smaller than that of FBP. (2) While the shape of the NPS of FBP was dose-independent, the shape of the NPS of MBIR was strongly dose-dependent; lower dose lead to a "redder" NPS with a lower mean frequency value. (3) The noise standard deviation (σ) of MBIR and dose were found to be related through a power law of σ ∝ (dose)(-β) with the component β ≈ 0.25, which violated the classical σ ∝ (dose)(-0.5) power law in FBP. (4) With MBIR, noise reduction was most prominent for thin image slices. (5) MBIR lead to better noise spatial uniformity when compared with FBP. (6) A composite image generated from two MBIR images acquired at two different dose levels (D1 and D2) demonstrated lower noise than that of an image acquired at a dose level of D1+D2.

CONCLUSIONS

The noise characteristics of the MBIR method are significantly different from those of the FBP method. The well known tradeoff relationship between CT image noise and radiation dose has been modified by MBIR to establish a more gradual dependence of noise on dose. Additionally, some other CT noise properties that had been well understood based on the linear system theory have also been altered by MBIR. Clinical CT scan protocols that had been optimized based on the classical CT noise properties need to be carefully re-evaluated for systems equipped with MBIR in order to maximize the method's potential clinical benefits in dose reduction and/or in CT image quality improvement.

Ordered subsets convex algorithm for 3D terahertz transmission tomography

We investigate in this paper a new reconstruction method in order to perform 3D Terahertz (THz) tomography using a continuous wave acquisition setup in transmission mode. This method is based on the Maximum Likelihood for TRansmission tomography (ML-TR) first developed for X-ray imaging. We optimize the Ordered Subsets Convex (OSC) implementation of the ML-TR by including the Gaussian propagation model of THz waves and take into account the intensity distributions of both blank calibration scan and dark-field measured on THz detectors. THz ML-TR reconstruction quality and accuracy are discussed and compared to other tomographic reconstructions.

TomoPy: a framework for the analysis of synchrotron tomographic data

Analysis of tomographic datasets at synchrotron light sources (including X-ray transmission tomography, X-ray fluorescence microscopy and X-ray diffraction tomography) is becoming progressively more challenging due to the increasing data acquisition rates that new technologies in X-ray sources and detectors enable. The next generation of synchrotron facilities that are currently under design or construction throughout the world will provide diffraction-limited X-ray sources and are expected to boost the current data rates by several orders of magnitude, stressing the need for the development and integration of efficient analysis tools. Here an attempt to provide a collaborative framework for the analysis of synchrotron tomographic data that has the potential to unify the effort of different facilities and beamlines performing similar tasks is described in detail. The proposed Python-based framework is open-source, platform- and data-format-independent, has multiprocessing capability and supports procedural programming that many researchers prefer. This collaborative platform could affect all major synchrotron facilities where new effort is now dedicated to developing new tools that can be deployed at the facility for real-time processing, as well as distributed to users for off-site data processing.

Adaptive nonlocal means filtering based on local noise level for CT denoising

PURPOSE

To develop and evaluate an image-domain noise reduction method based on a modified nonlocal means (NLM) algorithm that is adaptive to local noise level of CT images and to implement this method in a time frame consistent with clinical workflow.

METHODS

A computationally efficient technique for local noise estimation directly from CT images was developed. A forward projection, based on a 2D fan-beam approximation, was used to generate the projection data, with a noise model incorporating the effects of the bowtie filter and automatic exposure control. The noise propagation from projection data to images was analytically derived. The analytical noise map was validated using repeated scans of a phantom. A 3D NLM denoising algorithm was modified to adapt its denoising strength locally based on this noise map. The performance of this adaptive NLM filter was evaluated in phantom studies in terms of in-plane and cross-plane high-contrast spatial resolution, noise power spectrum (NPS), subjective low-contrast spatial resolution using the American College of Radiology (ACR) accreditation phantom, and objective low-contrast spatial resolution using a channelized Hotelling model observer (CHO). Graphical processing units (GPU) implementation of this noise map calculation and the adaptive NLM filtering were developed to meet demands of clinical workflow. Adaptive NLM was piloted on lower dose scans in clinical practice.

RESULTS

The local noise level estimation matches the noise distribution determined from multiple repetitive scans of a phantom, demonstrated by small variations in the ratio map between the analytical noise map and the one calculated from repeated scans. The phantom studies demonstrated that the adaptive NLM filter can reduce noise substantially without degrading the high-contrast spatial resolution, as illustrated by modulation transfer function and slice sensitivity profile results. The NPS results show that adaptive NLM denoising preserves the shape and peak frequency of the noise power spectrum better than commercial smoothing kernels, and indicate that the spatial resolution at low contrast levels is not significantly degraded. Both the subjective evaluation using the ACR phantom and the objective evaluation on a low-contrast detection task using a CHO model observer demonstrate an improvement on low-contrast performance. The GPU implementation can process and transfer 300 slice images within 5 min. On patient data, the adaptive NLM algorithm provides more effective denoising of CT data throughout a volume than standard NLM, and may allow significant lowering of radiation dose. After a two week pilot study of lower dose CT urography and CT enterography exams, both GI and GU radiology groups elected to proceed with permanent implementation of adaptive NLM in their GI and GU CT practices.

CONCLUSIONS

This work describes and validates a computationally efficient technique for noise map estimation directly from CT images, and an adaptive NLM filtering based on this noise map, on phantom and patient data. Both the noise map calculation and the adaptive NLM filtering can be performed in times that allow integration with clinical workflow. The adaptive NLM algorithm provides effective denoising of CT data throughout a volume, and may allow significant lowering of radiation dose.

Statistical model based iterative reconstruction (MBIR) in clinical CT systems. Part II. Experimental assessment of spatial resolution performance

PURPOSE

Statistical model based iterative reconstruction (MBIR) methods have been introduced to clinical CT systems and are being used in some clinical diagnostic applications. The purpose of this paper is to experimentally assess the unique spatial resolution characteristics of this nonlinear reconstruction method and identify its potential impact on the detectabilities and the associated radiation dose levels for specific imaging tasks.

METHODS

The thoracic section of a pediatric phantom was repeatedly scanned 50 or 100 times using a 64-slice clinical CT scanner at four different dose levels [CTDIvol =4, 8, 12, 16 (mGy)]. Both filtered backprojection (FBP) and MBIR (Veo(®), GE Healthcare, Waukesha, WI) were used for image reconstruction and results were compared with one another. Eight test objects in the phantom with contrast levels ranging from 13 to 1710 HU were used to assess spatial resolution. The axial spatial resolution was quantified with the point spread function (PSF), while the z resolution was quantified with the slice sensitivity profile. Both were measured locally on the test objects and in the image domain. The dependence of spatial resolution on contrast and dose levels was studied. The study also features a systematic investigation of the potential trade-off between spatial resolution and locally defined noise and their joint impact on the overall image quality, which was quantified by the image domain-based channelized Hotelling observer (CHO) detectability index d'.

RESULTS

(1) The axial spatial resolution of MBIR depends on both radiation dose level and image contrast level, whereas it is supposedly independent of these two factors in FBP. The axial spatial resolution of MBIR always improved with an increasing radiation dose level and/or contrast level. (2) The axial spatial resolution of MBIR became equivalent to that of FBP at some transitional contrast level, above which MBIR demonstrated superior spatial resolution than FBP (and vice versa); the value of this transitional contrast highly depended on the dose level. (3) The PSFs of MBIR could be approximated as Gaussian functions with reasonably good accuracy. (4) Thez resolution of MBIR showed similar contrast and dose dependence. (5) Noise standard deviation assessed on the edges of objects demonstrated a trade-off with spatial resolution in MBIR. (5) When both spatial resolution and image noise were considered using the CHO analysis, MBIR led to significant improvement in the overall CT image quality for both high and low contrast detection tasks at both standard and low dose levels.

CONCLUSIONS

Due to the intrinsic nonlinearity of the MBIR method, many well-known CT spatial resolution and noise properties have been modified. In particular, dose dependence and contrast dependence have been introduced to the spatial resolution of CT images by MBIR. The method has also introduced some novel noise-resolution trade-off not seen in traditional CT images. While the benefits of MBIR regarding the overall image quality, as demonstrated in this work, are significant, the optimal use of this method in clinical practice demands a thorough understanding of its unique physical characteristics.

Quantifying the Importance of the Statistical Assumption in Statistical X-ray CT Image Reconstruction

Statistical image reconstruction (SIR) is a promising approach to reducing radiation dose in clinical computerized tomography (CT) scans. Clinical CT scanners use energy-integrating detectors. The CT signal follows a compound Poisson distribution, its probability density function (PDF) does not have an analytical form hence cannot be used in an SIR method. The goal of this work is to quantify the effects of using an approximate statistical assumption in SIR methods for clinical CT applications. We apply a pseudo-Ideal Observer (pIO) to simulated CT projection data of the fanbeam geometry at different dose levels. The simulation models the polychromatic X-ray tube spectrum, the effects of the bowtie filter, and the energy-integrating detectors. The pIO uses a pseudo likelihood function (pLF) to calculate the pseudo likelihood ratio, which is the decision variable used by the pIO in a binary detection task. The pLF is an approximation to the true LF of the underlying data. The pIO has inferior performance than the IO unless the pLF coincides with the LF; this performance difference quantifies the closeness between the pseudo likelihood and the exact one. Using lesion detectability in a signal known exactly, background known exactly binary detection task as a figure-of-merit, our results show that at down to 0.1% of a reference tube current level I0, the pIO that uses a Poisson approximation, or a matched variance Gaussian approximation in either the transmission or the line integral domain, achieves 99% the performance of the IO. The constant variance Gaussian approximation has only 70%-80% of the IO performance. At tube currents lower than 0.1% I0, the performance difference is more substantial. We conclude that at current clinical dose levels, it is important to account for the mean-dependent variance in CT projection data in SIR problem formulation, the exact PDF of the CT signal is not as important.

Non-local means denoising of dynamic PET images

Objective

Dynamic positron emission tomography (PET), which reveals information about both the spatial distribution and temporal kinetics of a radiotracer, enables quantitative interpretation of PET data. Model-based interpretation of dynamic PET images by means of parametric fitting, however, is often a challenging task due to high levels of noise, thus necessitating a denoising step. The objective of this paper is to develop and characterize a denoising framework for dynamic PET based on non-local means (NLM).

Theory

NLM denoising computes weighted averages of voxel intensities assigning larger weights to voxels that are similar to a given voxel in terms of their local neighborhoods or patches. We introduce three key modifications to tailor the original NLM framework to dynamic PET. Firstly, we derive similarities from less noisy later time points in a typical PET acquisition to denoise the entire time series. Secondly, we use spatiotemporal patches for robust similarity computation. Finally, we use a spatially varying smoothing parameter based on a local variance approximation over each spatiotemporal patch.

Methods

To assess the performance of our denoising technique, we performed a realistic simulation on a dynamic digital phantom based on the Digimouse atlas. For experimental validation, we denoised PET images from a mouse study and a hepatocellular carcinoma patient study. We compared the performance of NLM denoising with four other denoising approaches – Gaussian filtering, PCA, HYPR, and conventional NLM based on spatial patches.

Results

The simulation study revealed significant improvement in bias-variance performance achieved using our NLM technique relative to all the other methods. The experimental data analysis revealed that our technique leads to clear improvement in contrast-to-noise ratio in Patlak parametric images generated from denoised preclinical and clinical dynamic images, indicating its ability to preserve image contrast and high intensity details while lowering the background noise variance.

Accelerating ordered subsets image reconstruction for X-ray CT using spatially nonuniform optimization transfer

Statistical image reconstruction algorithms in X-ray computed tomography (CT) provide improved image quality for reduced dose levels but require substantial computation time. Iterative algorithms that converge in few iterations and that are amenable to massive parallelization are favorable in multiprocessor implementations. The separable quadratic surrogate (SQS) algorithm is desirable as it is simple and updates all voxels simultaneously. However, the standard SQS algorithm requires many iterations to converge. This paper proposes an extension of the SQS algorithm that leads to spatially nonuniform updates. The nonuniform (NU) SQS encourages larger step sizes for the voxels that are expected to change more between the current and the final image, accelerating convergence, while the derivation of NU-SQS guarantees monotonic descent. Ordered subsets (OS) algorithms can also accelerate SQS, provided suitable "subset balance" conditions hold. These conditions can fail in 3-D helical cone-beam CT due to incomplete sampling outside the axial region-of-interest (ROI). This paper proposes a modified OS algorithm that is more stable outside the ROI in helical CT. We use CT scans to demonstrate that the proposed NU-OS-SQS algorithm handles the helical geometry better than the conventional OS methods and "converges" in less than half the time of ordinary OS-SQS.

Characterization of a constrained paired-view technique in iterative reconstruction for breast tomosynthesis

PURPOSE

The order in which the projection views are employed in the reconstruction of tomosynthesis by iterative algorithms, such as simultaneous algebraic reconstruction technique and maximum likelihood, has a strong effect on the rate of convergence, accuracy, and the edge-blurring artifacts in the reconstructed image. The purpose of this investigation was to characterize and evaluate the effects of ordering schemes on image quality for breast tomosynthesis reconstruction and to explore a new constrained paired-view technique that could provide reduction of reconstruction artifacts. In this work, the authors compared several different ordering schemes and characterized the image quality and the formation of out-of-plane artifacts. Furthermore, a new normalization method is presented. It produces more accurate reconstructions with reduced artifacts comparing to the standard method of sequential ordering.

METHODS

In addition to visual assessment of image quality, several indices such as the signal-difference-to-noise ratio, the artifact-spread function, and the lesion detectability (d(')) were computed to quantitatively evaluate the effect of ordering scheme. The sets of breast tomosynthesis projection images were simulated for reconstruction; one set had uniform background (white noise only) and the other two contained both anatomic background and quantum noise. Clinical breast images were also studied for comparison.

RESULTS

The authors have quantified the image quality in reconstructed slices for a range of tumor sizes. The authors' proposed method provides better performance for all of the metrics tested (contrast, d('), and the level of artifacts) both for the uniform phantom case and in the presence of anatomical structure.

CONCLUSIONS

The paired projection normalization provides better performance in the image quality of the reconstructed slices, and results in a lower level of artifacts in the Z direction. This implies that even a relatively simple method like the "side-to-side" sequence, which pairs two symmetrical projections with equal angular distance from the central projection, would achieve better reconstructed image quality than the conventional "step-by-step" method, which uses sequential projections one after another.

Patchwork reconstruction with resolution modeling for digital breast tomosynthesis

PURPOSE

Digital breast tomosynthesis is a relatively new diagnostic x-ray modality that allows high resolution breast imaging while suppressing interference from overlapping anatomical structures. However, proper visualization of microcalcifications remains a challenge. For the subset of systems considered by the authors, the main cause of deterioration is movement of the x-ray source during exposures. They propose a modified grouped coordinate ascent algorithm that includes a specific acquisition model to compensate for this deterioration.

METHODS

A resolution model based on the movement of the x-ray source during image acquisition is created and combined with a grouped coordinate ascent algorithm. Choosing planes parallel to the detector surface as the groups enables efficient implementation of the position dependent resolution model. In the current implementation, the resolution model is approximated by a Gaussian smoothing kernel. The effect of the resolution model on the iterative reconstruction is evaluated by measuring contrast to noise ratio (CNR) of spherical microcalcifications in a homogeneous background. After this, the new reconstruction method is compared to the optimized filtered backprojection method for the considered system, by performing two observer studies: the first study simulates clusters of spherical microcalcifications in a power law background for a free search task; the second study simulates smooth or irregular microcalcifications in the same type of backgrounds for a classification task.

RESULTS

Including the resolution model in the iterative reconstruction methods increases the CNR of microcalcifications. The first observer study shows a significant improvement in detection of microcalcifications (p = 0.029), while the second study shows that performance on a classification task remains the same (p = 0.935) compared to the filtered backprojection method.

CONCLUSIONS

The new method shows higher CNR and improved visualization of microcalcifications in an observer experiment on synthetic data. Further study of the negative results of the classification task showed performance variations throughout the volume linked to the changing noise structure introduced by the combination of the resolution model and the smoothing prior.

Mass detection in reconstructed digital breast tomosynthesis volumes with a computer-aided detection system trained on 2D mammograms

PURPOSE

To develop a computer-aided detection (CAD) system for masses in digital breast tomosynthesis (DBT) which can make use of an existing CAD system for detection of breast masses in full-field digital mammography (FFDM). This approach has the advantage that large digital screening databases that are becoming available can be used for training. DBT is currently not used for screening which makes it hard to obtain sufficient data for training.

METHODS

The proposed CAD system is applied to reconstructed DBT volumes and consists of two stages. In the first stage, an existing 2D CAD system is applied to slabs composed of multiple DBT slices, after processing the slabs to a representation similar to that of the FFDM training data. In the second stage, the authors group detections obtained in the slabs that detect the same object and determine the 3D location of the grouped findings using one of three different approaches, including one that uses a set of features extracted from the DBT slabs. Experiments were conducted to determine performance of the CAD system, the optimal slab thickness for this approach and the best method to establish the 3D location. Experiments were performed using a database of 192 patients (752 DBT volumes). In 49 patients, one or more malignancies were present which were described as a mass, architectural distortion, or asymmetry. Free response receiver operating characteristic analysis and bootstrapping were used for statistical evaluation.

RESULTS

Best performance was obtained when slab thickness was in the range of 1-2 cm. Using the feature based 3D localization procedure developed in the study, accurate 3D localization could be obtained in most cases. Case sensitivities of 80% and 90% were achieved at 0.35 and 0.99 false positives per volume, respectively.

CONCLUSIONS

This study indicates that there may be a large benefit in using 2D mammograms for the development of CAD for DBT and that there is no need to exclusively limit development to DBT data.

Information-theoretic discrepancy based iterative reconstructions (IDIR) for polychromatic x-ray tomography

PURPOSE

X-ray photons generated from a typical x-ray source for clinical applications exhibit a broad range of wavelengths, and the interactions between individual particles and biological substances depend on particles' energy levels. Most existing reconstruction methods for transmission tomography, however, neglect this polychromatic nature of measurements and rely on the monochromatic approximation. In this study, we developed a new family of iterative methods that incorporates the exact polychromatic model into tomographic image recovery, which improves the accuracy and quality of reconstruction.

METHODS

The generalized information-theoretic discrepancy (GID) was employed as a new metric for quantifying the distance between the measured and synthetic data. By using special features of the GID, the objective function for polychromatic reconstruction which contains a double integral over the wavelength and the trajectory of incident x-rays was simplified to a paraboloidal form without using the monochromatic approximation. More specifically, the original GID was replaced with a surrogate function with two auxiliary, energy-dependent variables. Subsequently, the alternating minimization technique was applied to solve the double minimization problem. Based on the optimization transfer principle, the objective function was further simplified to the paraboloidal equation, which leads to a closed-form update formula. Numerical experiments on the beam-hardening correction and material-selective reconstruction were conducted to compare and assess the performance of conventional methods and the proposed algorithms.

RESULTS

The authors found that the GID determines the distance between its two arguments in a flexible manner. In this study, three groups of GIDs with distinct data representations were considered. The authors demonstrated that one type of GIDs that comprises "raw" data can be viewed as an extension of existing statistical reconstructions; under a particular condition, the GID is equivalent to the Poisson log-likelihood function. The newly proposed GIDs of the other two categories consist of log-transformed measurements, which have the advantage of imposing linearized penalties over multiple discrepancies. For all proposed variants of the GID, the aforementioned strategy was used to obtain a closed-form update equation. Even though it is based on the exact polychromatic model, the derived algorithm bears a structural resemblance to conventional methods based on the monochromatic approximation. The authors named the proposed approach as information-theoretic discrepancy based iterative reconstructions (IDIR). In numerical experiments, IDIR with raw data converged faster than previously known statistical reconstruction methods. IDIR with log-transformed data exhibited superior reconstruction quality and faster convergence speed compared with conventional methods and their variants.

CONCLUSIONS

The authors' new framework for tomographic reconstruction allows iterative inversion of the polychromatic data model. The primary departure from the traditional iterative reconstruction was the employment of the GID as a new metric for quantifying the inconsistency between the measured and synthetic data. The proposed methods outperformed not only conventional methods based on the monochromatic approximation but also those based on the polychromatic model. The authors have observed that the GID is a very flexible means to design an objective function for iterative reconstructions. Hence, the authors expect that the proposed IDIR framework will also be applicable to other challenging tasks.

Parameter optimization of relaxed Ordered Subsets Pre-computed Back Projection (BP) based Penalized-Likelihood (OS-PPL) reconstruction in limited-angle X-ray tomography

This paper presents a two-step strategy to provide a quality-predictable image reconstruction. A Pre-computed Back Projection based Penalized-Likelihood (PPL) method is proposed in the strategy to generate consistent image quality. To solve PPL efficiently, relaxed Ordered Subsets (OS) is applied. A training sets based evaluation is performed to quantify the effect of the undetermined parameters in OS, which lets the results as consistent as possible with the theoretical one.

A review of breast tomosynthesis. Part II. Image reconstruction, processing and analysis, and advanced applications

Many important post-acquisition aspects of breast tomosynthesis imaging can impact its clinical performance. Chief among them is the reconstruction algorithm that generates the representation of the three-dimensional breast volume from the acquired projections. But even after reconstruction, additional processes, such as artifact reduction algorithms, computer aided detection and diagnosis, among others, can also impact the performance of breast tomosynthesis in the clinical realm. In this two part paper, a review of breast tomosynthesis research is performed, with an emphasis on its medical physics aspects. In the companion paper, the first part of this review, the research performed relevant to the image acquisition process is examined. This second part will review the research on the post-acquisition aspects, including reconstruction, image processing, and analysis, as well as the advanced applications being investigated for breast tomosynthesis.

Towards high-resolution synchrotron radiation imaging with statistical iterative reconstruction

Synchrotron radiation (SR) X-ray micro-computed tomography (CT) is an effective imaging modality for high-resolution investigation of small objects, with several applications in medicine, biology and industry. However, the limited size of the detector field of view (FOV) restricts the sample dimensions to only a few millimeters. When the sample size is larger than the FOV, images reconstructed using conventional methods suffer from DC-shift and low-frequency artifacts. This classical problem is known as the local tomography or the interior problem. In this paper, a statistical iterative reconstruction method is introduced to eliminate image artifacts resulting from the local tomography. The proposed method, which can be used in several SR imaging applications, enables high-resolution SR imaging with superior image quality compared with conventional methods. Real data obtained from different SR micro-CT applications are used to evaluate the proposed method. Results indicate a noteworthy quality improvement in the image reconstructed from the local tomography measurements.

Toward truly combined PET/CT imaging using PET detectors and photon counting CT with iterative reconstruction implementing physical detector response

PURPOSE

This paper intends to demonstrate the feasibility of truly combined PET/CT imaging and addresses some of the major challenges raised by this dual modality approach. A method is proposed to retrieve maximum accuracy out of limited resolution computed tomography (CT) scans acquired with positron emission tomography (PET) detectors.

METHODS

A PET/CT simulator was built using the LabPET™ detectors and front-end electronics. Acquisitions of energy-binned data sets were made using this low spatial resolution CT system in photon counting mode. To overcome the limitations of the filtered back-projection technique, an iterative reconstruction library was developed and tested for the counting mode CT. Construction of the system matrix is based on a preregistered raster scan from which the experimental detector response is obtained. PET data were obtained sequentially with CT in a conventional manner.

RESULTS

A meticulous description of the system geometry and misalignment corrections is imperative and was incorporated into the matrix definition to achieve good image quality. Using this method, no sinogram precorrection or interpolation is necessary and measured projections can be used as raw input data for the iterative reconstruction algorithm. Genuine dual modality PET/CT images of phantoms and animals were obtained for the first time using the same detection platform.

CONCLUSIONS

CT and fused PET/CT images show that LabPET™ detectors can be successfully used as individual X-ray photon counting devices for low-dose CT imaging of the anatomy in a molecular PET imaging context.