Iterative image reconstruction algorithm analysis for optical CT radiochromic gel dosimetry

Background.Modern radiation therapy technologies aim to enhance radiation dose precision to the tumor and utilize hypofractionated treatment regimens. Verifying the dose distributions associated with these advanced radiation therapy treatments remains an active research area due to the complexity of delivery systems and the lack of suitable three-dimensional dosimetry tools. Gel dosimeters are a potential tool for measuring these complex dose distributions. A prototype tabletop solid-tank fan-beam optical CT scanner for readout of gel dosimeters was recently developed. This scanner does not have a straight raypath from source to detector, thus images cannot be reconstructed using filtered backprojection (FBP) and iterative techniques are required.Purpose.To compare a subset of the top performing algorithms in terms of image quality and quantitatively determine the optimal algorithm while accounting for refraction within the optical CT system. The following algorithms were compared: Landweber, superiorized Landweber with the fast gradient projection perturbation routine (S-LAND-FGP), the fast iterative shrinkage/thresholding algorithm with total variation penalty term (FISTA-TV), a monotone version of FISTA-TV (MFISTA-TV), superiorized conjugate gradient with the nonascending perturbation routine (S-CG-NA), superiorized conjugate gradient with the fast gradient projection perturbation routine (S-CG-FGP), superiorized conjugate gradient with with two iterations of CG performed on the current iterate and the nonascending perturbation routine (S-CG-2-NA).Methods.A ray tracing simulator was developed to track the path of light rays as they traverse the different mediums of the optical CT scanner. Two clinical phantoms and several synthetic phantoms were produced and used to evaluate the reconstruction techniques under known conditions. Reconstructed images were analyzed in terms of spatial resolution, signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), signal non-uniformity (SNU), mean relative difference (MRD) and reconstruction time. We developed an image quality based method to find the optimal stopping iteration window for each algorithm. Imaging data from the prototype optical CT scanner was reconstructed and analysed to determine the optimal algorithm for this application.Results.The optimal algorithms found through the quantitative scoring metric were FISTA-TV and S-CG-2-NA. MFISTA-TV was found to behave almost identically to FISTA-TV however MFISTA-TV was unable to resolve some of the synthetic phantoms. S-CG-NA showed extreme fluctuations in the SNR and CNR values. S-CG-FGP had large fluctuations in the SNR and CNR values and the algorithm has less noise reduction than FISTA-TV and worse spatial resolution than S-CG-2-NA. S-LAND-FGP had many of the same characteristics as FISTA-TV; high noise reduction and stability from over iterating. However, S-LAND-FGP has worse SNR, CNR and SNU values as well as longer reconstruction time. S-CG-2-NA has superior spatial resolution to all algorithms while still maintaining good noise reduction and is uniquely stable from over iterating.Conclusions.Both optimal algorithms (FISTA-TV and S-CG-2-NA) are stable from over iterating and have excellent edge detection with ESF MTF 50% values of 1.266 mm-1and 0.992 mm-1. FISTA-TV had the greatest noise reduction with SNR, CNR and SNU values of 424, 434 and 0.91 × 10-4, respectively. However, low spatial resolution makes FISTA-TV only viable for large field dosimetry. S-CG-2-NA has better spatial resolution than FISTA-TV with PSF and LSF MTF 50% values of 1.581 mm-1and 0.738 mm-1, but less noise reduction. S-CG-2-NA still maintains good SNR, CNR, and SNU values of 168, 158 and 1.13 × 10-4, respectively. Thus, S-CG-2-NA is a well rounded reconstruction algorithm that would be the preferable choice for small field dosimetry.

Iterative image reconstruction with polar coordinate discretized system matrix for optical CT radiochromic gel dosimetry

BACKGROUND

Gel dosimeters are a potential tool for measuring the complex dose distributions that characterize modern radiotherapy. A prototype tabletop solid-tank fan-beam optical CT scanner for readout of gel dosimeters was recently developed. This scanner does not have a straight raypath from source to detector, thus images cannot be reconstructed using filtered backprojection (FBP) and iterative techniques are required. Iterative image reconstruction requires a system matrix that describes the geometry of the imaging system. Stored system matrices can become immensely large, making them impractical for storage on a typical desktop computer.

PURPOSE

Here we develop a method to reduce the storage size of optical CT system matrices through use of polar coordinate discretization while accounting for the refraction in optical CT systems.

METHODS

A ray tracing simulator was developed to track the path of light rays as they traverse the different mediums of the optical CT scanner. Cartesian coordinate discretized system matrices (CCDSMs) and polar coordinate discretized system matrices (PCDSMs) were generated by discretizing the reconstruction area of the optical CT scanner into a Cartesian pixel grid and a polar coordinate pixel grid, respectively. The length of each ray through each pixel was calculated and used to populate the system matrices. To ensure equal weighting during iterative reconstruction, the radial rings of PCDSMs were asymmetrically spaced such that the area of each polar pixel was constant. Two clinical phantoms and several synthetic phantoms were produced and used to evaluate the reconstruction techniques under known conditions. Reconstructed images were analyzed in terms of spatial resolution, signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), signal nonuniformity (SNU), and Gamma map pass percentage.

RESULTS

A storage size reduction of 99.72% was found when comparing a PCDSM to a CCDSM with the same total number of pixels. Images reconstructed with a PCDSM were found to have superior SNR, CNR, SNU, and Gamma (1 mm, 1%) pass percentage compared to those reconstructed with a CCDSM. Increasing spatial resolution in the radial direction with increasing radial distance was found in both PCDSM and CCDSM reconstructions due to the outer regions refracting light more severely. Images reconstructed with a PCDSM showed a decrease in spatial resolution in the azimuthal directions as radial distance increases, due to the widening of the polar pixels. However, this can be mitigated with only a slight increase in storage size by increasing the number of projections. A loss of spatial resolution in the radial direction within 5 mm radially from center was found when reconstructing with a PCDSM, due to the large innermost pixels. However, this was remedied by increasing the number of radial rings within the PCDSM, yielding radial spatial resolution on par with images reconstructed with a CCDSM and a storage size reduction of 99.26%.

CONCLUSIONS

Discretizing the image pixel elements in polar coordinates achieved a system matrix storage size reduction of 99.26% with only minimal reduction in the image quality.

A fast tomosynthesis method for printed circuit boards based on a multiple multi-resolution reconstruction algorithm

Digital tomosynthesis (DTS) technology has attracted much attention in the field of nondestructive testing of printed circuit boards (PCB) due to its high resolution and suitability to thin slab objects. However, the traditional DTS iterative algorithm is computationally demanding, and its real-time processing of high-resolution and large volume reconstruction is infeasible. To address this issue, we in this study propose a multiple multi-resolution algorithm, including two multi-resolution strategies: volume domain multi-resolution and projection domain multi-resolution. The first multi-resolution scheme employs a LeNet-based classification network to divide the roughly reconstructed low-resolution volume into two sub-volumes namely, (1) the region of interest (ROI) with welding layers that necessitates high-resolution reconstruction, and (2) the remaining volume with unimportant information which can be reconstructed in low-resolution. When X-rays in adjacent projection angles pass through many identical voxels, information redundancy is prevalent between the adjacent image projections. Therefore, the second multi-resolution scheme divides the projections into non-overlapping subsets, using only one subset for each iteration. The proposed algorithm is evaluated using both the simulated and real image data. The results demonstrate that the proposed algorithm is approximately 6.5 times faster than the full-resolution DTS iterative reconstruction algorithm without compromising image reconstruction quality.

Physics-Driven Deep Learning for Computational Magnetic Resonance Imaging: Combining physics and machine learning for improved medical imaging

Physics-driven deep learning methods have emerged as a powerful tool for computational magnetic resonance imaging (MRI) problems, pushing reconstruction performance to new limits. This article provides an overview of the recent developments in incorporating physics information into learning-based MRI reconstruction. We consider inverse problems with both linear and non-linear forward models for computational MRI, and review the classical approaches for solving these. We then focus on physics-driven deep learning approaches, covering physics-driven loss functions, plug-and-play methods, generative models, and unrolled networks. We highlight domain-specific challenges such as real- and complex-valued building blocks of neural networks, and translational applications in MRI with linear and non-linear forward models. Finally, we discuss common issues and open challenges, and draw connections to the importance of physics-driven learning when combined with other downstream tasks in the medical imaging pipeline.

Isotropic multichannel total variation framework for joint reconstruction of multicontrast parallel MRI

Purpose: To develop a synergistic image reconstruction framework that exploits multicontrast (MC), multicoil, and compressed sensing (CS) redundancies in magnetic resonance imaging (MRI). Approach: CS, MC acquisition, and parallel imaging (PI) have been individually well developed, but the combination of the three has not been equally well studied, much less the potential benefits of isotropy within such a setting. Inspired by total variation theory, we introduce an isotropic MC image regularizer and attain its full potential by integrating it into compressed MC multicoil MRI. A convex optimization problem is posed to model the new variational framework and a first-order algorithm is developed to solve the problem. Results: It turns out that the proposed isotropic regularizer outperforms many of the state-of-the-art reconstruction methods not only in terms of rotation-invariance preservation of symmetrical features, but also in suppressing noise or streaking artifacts, which are normally encountered in PI methods at aggressive undersampling rates. Moreover, the new framework significantly prevents intercontrast leakage of contrast-specific details, which seems to be a difficult situation to handle for some variational and low-rank MC reconstruction approaches. Conclusions: The new framework is a viable option for image reconstruction in fast protocols of MC parallel MRI, potentially reducing patient discomfort in otherwise long and time-consuming scans.

Lutetium background radiation in total-body PET-A simulation study on opportunities and challenges in PET attenuation correction

The current generation of total-body positron emission tomography (PET) scanners offer significant sensitivity increase with an extended axial imaging extent. With the large volume of lutetium-based scintillation crystals that are used as detector elements in these scanners, there is an increased flux of background radiation originating from ¹⁷⁶Lu decay in the crystals and higher sensitivity for detecting it. Combined with the ability of scanning the entire body in a single bed position, this allows more effective utilization of the lutetium background as a transmission source for estimating 511 keV attenuation coefficients. In this study, utilization of the lutetium background radiation for attenuation correction in total-body PET was studied using Monte Carlo simulations of a 3D whole-body XCAT phantom in the uEXPLORER PET scanner, with particular focus on ultralow-dose PET scans that are now made possible with these scanners. Effects of an increased acceptance angle, reduced scan durations, and Compton scattering on PET quantification were studied. Furthermore, quantification accuracy of lutetium-based attenuation correction was compared for a 20-min scan of the whole body on the uEXPLORER, a one-meter-long, and a conventional 24-cm-long scanner. Quantification and lesion contrast were minimally affected in both long axial field-of-view scanners and in a whole-body 20-min scan, the mean bias in all analyzed organs of interest were within a ±10% range compared to ground-truth activity maps. Quantification was affected in certain organs, when scan duration was reduced to 5 min or a reduced acceptance angle of 17° was used. Analysis of the Compton scattered events suggests that implementing a scatter correction method for the transmission data will be required, and increasing the energy threshold from 250 keV to 290 keV can reduce the computational costs and data rates, with negligible effects on PET quantification. Finally, the current results can serve as groundwork for transferring lutetium-based attenuation correction into research and clinical practice.

Iterative reconstruction improves image quality and reduces radiation dose in trauma protocols; A human cadaver study

Background

Radiation-related cancer risk is an object of concern in CT of trauma patients, as these represent a young population. Different radiation reducing methods, including iterative reconstruction (IR), and spilt bolus techniques have been introduced in the recent years in different large scale trauma centers.

Purpose

To compare image quality in human cadaver exposed to thoracoabdominal computed tomography using IR and standard filtered back-projection (FBP) at different dose levels.

Material and methods

Ten cadavers were scanned at full dose and a dose reduction in CTDIvol of 5 mGy (low dose 1) and 7.5 mGy (low dose 2) on a Siemens Definition Flash 128-slice computed tomography scanner. Low dose images were reconstructed with FBP and Sinogram affirmed iterative reconstruction (SAFIRE) level 2 and 4. Quantitative image quality was analyzed by comparison of contrast-to-noise ratio (CNR) and signal-to-noise ratio (SNR). Qualitative image quality was evaluated by use of visual grading regression (VGR) by four radiologists.

Results

Readers preferred SAFIRE reconstructed images over FBP at a dose reduction of 40% (low dose 1) and 56% (low dose 2), with significant difference in overall impression of image quality. CNR and SNR showed significant improvement for images reconstructed with SAFIRE 2 and 4 compared to FBP at both low dose levels.

Conclusions

Iterative image reconstruction, SAFIRE 2 and 4, resulted in equal or improved image quality at a dose reduction of up to 56% compared to full dose FBP and may be used a strong radiation reduction tool in the young trauma population.

Reducing residual-motion artifacts in iterative 3D CBCT reconstruction in image-guided radiation therapy

PURPOSE

Recent evaluations of a 3D iterative cone-beam computed tomography (iCBCT) reconstruction method available on Varian radiation treatment devices demonstrated that iCBCT provides superior image quality when compared to analytical Feldkamp-Davis-Kress (FDK) method. However, iCBCT employs statistical penalized likelihood (PL) that is known to be highly sensitive to inconsistencies due to physiological motion occurring during the acquisition. We propose a computationally inexpensive extension of iCBCT addressing this deficiency.

METHODS

During the iterative process, the gradients of PL are modified to avoid the generation of motion-related artifacts. To assess the impact of this modification, we propose a motion simulation generating CBCT projections of a moving anatomy together with artifact-free images used as ground truth. Contrast-to-noise ratio and power spectra of difference images are computed to quantify the impact of the motion on reconstructed CBCT volumes as well as the effect of the proposed modification.

RESULTS

Using both simulated and clinical data, it is shown that the motion of patient's abdominal wall during the acquisition results in artifacts that can be quantified as low-frequency components in volumes reconstructed with iCBCT. Further, a quantitative evaluation demonstrates that the proposed modification of PL reduces these low-frequency components. While preserving the advantages of PL, it effectively suppresses the propagation of motion-related artifacts into clinically important regions, thus increasing the motion resiliency of iCBCT.

CONCLUSIONS

The proposed modified iterative reconstruction method significantly improves the quality of CBCT images of anatomies suffering from residual motion.

Systematic evaluation of iterative deep neural networks for fast parallel MRI reconstruction with sensitivity-weighted coil combination

PURPOSE

To systematically investigate the influence of various data consistency layers and regularization networks with respect to variations in the training and test data domain, for sensitivity-encoded accelerated parallel MR image reconstruction.

THEORY AND METHODS

Magnetic resonance (MR) image reconstruction is formulated as a learned unrolled optimization scheme with a down-up network as regularization and varying data consistency layers. The proposed networks are compared to other state-of-the-art approaches on the publicly available fastMRI knee and neuro dataset and tested for stability across different training configurations regarding anatomy and number of training samples.

RESULTS

Data consistency layers and expressive regularization networks, such as the proposed down-up networks, form the cornerstone for robust MR image reconstruction. Physics-based reconstruction networks outperform post-processing methods substantially for R = 4 in all cases and for R = 8 when the training and test data are aligned. At R = 8, aligning training and test data is more important than architectural choices.

CONCLUSION

In this work, we study how dataset sizes affect single-anatomy and cross-anatomy training of neural networks for MRI reconstruction. The study provides insights into the robustness, properties, and acceleration limits of state-of-the-art networks, and our proposed down-up networks. These key insights provide essential aspects to successfully translate learning-based MRI reconstruction to clinical practice, where we are confronted with limited datasets and various imaged anatomies.

Improved Reliability of Automated ASPECTS Evaluation Using Iterative Model Reconstruction from Head CT Scans

BACKGROUND AND PURPOSE

Iterative model reconstruction (IMR) has shown to improve computed tomography (CT) image quality compared to hybrid iterative reconstruction (HIR). Alberta Stroke Program Early CT Score (ASPECTS) assessment in early stroke is particularly dependent on high-image quality. Purpose of this study was to investigate the reliability of ASPECTS assessed by humans and software based on HIR and IMR, respectively.

METHODS

Forty-seven consecutive patients with acute anterior circulation large vessel occlusions (LVOs) and successful endovascular thrombectomy were included. ASPECTS was assessed by three neuroradiologists (one attending, two residents) and by automated software in noncontrast axial CT with HIR (iDose4; 5 mm) and IMR (5 and 0.9 mm). Two expert neuroradiologists determined consensus ASPECTS reading using all available image data including MRI. Agreement between four raters (three humans, one software) and consensus were compared using square-weighted kappa (κ).

RESULTS

Human raters achieved moderate to almost perfect agreement (κ = .557-.845) with consensus reading. The attending showed almost perfect agreement for 5 mm HIR (κ_HIR  = .845), while residents had mostly substantial agreements without clear trends across reconstructions. Software had substantial to almost perfect agreement with consensus, increasing with IMR 5 and 0.9 mm slice thickness (κ_HIR  = .751, κ_IMR  = .777, and κ_IMR0.9  = .814). Agreements inversely declined for these reconstructions for the attending (κ_HIR  = .845, κ_IMR  = .763, and κ_IMR0.9  = .681).

CONCLUSIONS

Human and software rating showed good reliability of ASPECTS across different CT reconstructions. Human raters performed best with the reconstruction algorithms they had most experience with (HIR for the attending). Automated software benefits from higher resolution with better contrasts in IMR with 0.9 mm slice thickness.

Computationally Efficient System Matrix Calculation Techniques in Computed Tomography Iterative Reconstruction

Background:

Relative to classical methods in computed tomography, iterative reconstruction techniques enable significantly improved image qualities and/or lowered patient doses. However, the computational speed is a major concern for these iterative techniques. In the present study, we present a method for fast system matrix calculation based on the line integral model (LIM) to speed up the computations without compromising the image quality. In addition, we develop a hybrid line–area integral model (AIM) that highlights the advantages of both LIM and AIMs.

Methods:

The contributing detectors for a given pixel and a given projection view, and the length of corresponding intersection lines with pixels, are calculated using our proposed algorithm. For the hybrid method, the respective narrow-angle fan beam was modeled by multiple equally spaced lines. The computed system matrix was evaluated in the context of reconstruction using the simultaneous algebraic reconstruction technique (SART) as well as maximum likelihood expectation maximization (MLEM).

Results:

The proposed LIM offers a considerable reduction in calculation times compared to the standard Siddon algorithm: 2.9 times faster. Differences in root mean square error and peak signal-to-noise ratio were not significant between the proposed LIM and the Siddon algorithm for both SART and MLEM reconstruction methods (P > 0.05). Meanwhile, the proposed hybrid method resulted in significantly improved image qualities relative to LIM and the Siddon algorithm (P < 0.05), though computations were 4.9 times more intensive than the proposed LIM.

Conclusion:

We have proposed two fast algorithms to calculate the system matrix. The first is based on LIM and was faster than the Siddon algorithm, with matched image quality, whereas the second method is a hybrid LIM–AIM that achieves significantly improved images though with its computational requirements.

[Incident Photon Number and Reconstructed Linear Attenuation Coefficients in Iterative CT Image Reconstruction]

[Purpose] The iterative CT image reconstruction (IR) method has been successfully incorporated into commercial CT scanners as a means to promote low-dose CT with high image quality. However, the algorithm of the IR method has not been made publicly available by scanner manufacturers. Kudo reviewed the fundamentals of IR methods on the basis of the articles published by the joint research group of each manufacture that were released before and during product development (Med Imag Tech 32: 239-248, 2014). According to this review, the object function of the IR method consists of the data fidelity term (likelihood) and the regularization term. The regularization term plays a significant role in the IR method; however, it has not been clarified whether or not the variance of projection data should be included into the likelihood to act the regularization term effectively. Our purpose in this study was to investigate the relationship of the incident photon number and the reconstructed linear attenuation coefficients of the IR method by numerical experiments.[Methods] We assumed the X-ray beam was a pencil beam, and the system matrix was given by the line integral of linear attenuation coefficients because we focused on the accuracy of the reconstructed linear attenuation coefficients in the ideal photon detection system equations given by Kudo. Total variation (TV) and the relative difference function were used for regularization of the IR method. Three kinds of numerical phantoms with 256×256 pixels were used as test images. Poisson noise was added to the projection data with 256 linear sampling and 256 views over 180°. The accuracy of reconstructed linear attenuation coefficients was evaluated by the mean reconstructed value within a region of interest (ROI) and the relative root mean square errors (%RMSEs) to the object image.[Results] The linear attenuation coefficients were reconstructed accurately by the IR method including the variance of projection data into the likelihood in comparison with the IR method without including the variance. When the incident photon number ranged from 100 to 2000 for the object having a mean linear attenuation coefficient of 0.067 to 0.087 cm^-1, the reconstructed linear attenuation coefficients in ROI were close to the true values. However, when the incident photon number was 50, both the accuracy and the uniformity of reconstructed images decreased.[Discussion] From the viewpoint of the visual observation, the image quality of the IR method was superior to that of the filtered back-projection (FBP) image processed with the Gaussian filter of FWHM equal to 3 pixels. For the object with a high absorber, the FBP gives linear attenuation coefficients that were lower than the true values. This phenomenon was also observed in the IR method. The projection data of CT were given by the logarithm operation of the ratio between the incident photon and the transmitted photon numbers. If the transmitted photon number happened to be equal to 0 owing to the influence of noise, it was held to a value of 1 to avoid the logarithm of zero. This process caused an error of the linear attenuation coefficients.[Conclusion] The variance of projection data should be included into the likelihood to act the regularization term effectively in the IR method.

Assessment of the generalization of learned image reconstruction and the potential for transfer learning

PURPOSE

Although deep learning has shown great promise for MR image reconstruction, an open question regarding the success of this approach is the robustness in the case of deviations between training and test data. The goal of this study is to assess the influence of image contrast, SNR, and image content on the generalization of learned image reconstruction, and to demonstrate the potential for transfer learning.

METHODS

Reconstructions were trained from undersampled data using data sets with varying SNR, sampling pattern, image contrast, and synthetic data generated from a public image database. The performance of the trained reconstructions was evaluated on 10 in vivo patient knee MRI acquisitions from 2 different pulse sequences that were not used during training. Transfer learning was evaluated by fine-tuning baseline trainings from synthetic data with a small subset of in vivo MR training data.

RESULTS

Deviations in SNR between training and testing led to substantial decreases in reconstruction image quality, whereas image contrast was less relevant. Trainings from heterogeneous training data generalized well toward the test data with a range of acquisition parameters. Trainings from synthetic, non-MR image data showed residual aliasing artifacts, which could be removed by transfer learning-inspired fine-tuning.

CONCLUSION

This study presents insights into the generalization ability of learned image reconstruction with respect to deviations in the acquisition settings between training and testing. It also provides an outlook for the potential of transfer learning to fine-tune trainings to a particular target application using only a small number of training cases.

[An Error Evaluation of Iterative Image Reconstruction Methods Using Chi-Square (χ2) Statistic Minimization for Poisson-Distributed Projection Data]

[Purpose] Iterative image reconstruction (IR) methods using Neyman's chi-square statistic (χ²_N) or Pearson's chi-square statistic (χ²_P) have been investigated in nuclear medicine. However, these chi-square statistic-based image reconstructions have never been installed on clinical nuclear medicine instruments. Mighell developed another chi-square statistic (χ²_M). Recently, Mighell's chi-square statistic has been incorporated into commercial SPECT instrument aiming at high accuracy in the iterative image reconstruction from low count projection data. However, the error evaluation for χ²_M was not reported by the instrument manufacturer or the joint research group involved in the product development. Therefore, it is not certain to what extent χ²_M is superior to χ²_N or χ²_P. In this study we investigated the accuracy of the chi-square statistic-based IR methods by computer simulation.[Methods] We used two kinds of numerical phantoms (256×256 pixels) for testing root mean square error (RMSE). Phantom A was a disk that was 18.4 cm in diameter and the count density was varied from 1 count/pixel to 10 counts/pixel at intervals of 1 count/pixel in each trial. Phantom B was a disk that was 18.4 cm in diameter and the count densities for the seven disk inserts (diameter 3 cm) which were investigated were 1, 2, 3, 4, 5, 6, and 7 counts/pixel. Poisson noise was added to the projection data with 256 linear samplings and 256 views over 180°. Projection data were assumed to be without attenuation and scatter effects, because we focused our evaluation on the noise propagation from projection data to the reconstructed image that was attributable to the mathematical equations of the different types of chi-square statistic. Minimization of the chi-square statistic-based IR methods was performed by conjugate gradient method.[Results] We found the noise was suppressed by including the variance of projection data in each chi-square statistic; however, it was not suppressed sufficiently by χ²_P in comparison with χ²_N and χ²_M. For 1000 iterations, the RMSEs of Phantom A having the count density of 1 count/pixel were 21.46±2.75, 39.21±0.71, and 12.29±0.63, obtained by χ²_N, χ²_P, and χ²_M in 20 trials, respectively. For 2 counts/pixel, RMSEs were 5.26±0.32, 19.89±1.29, and 4.23±0.08; and for 3 counts/pixel, they were 5.34±0.56, 10.27±0.38, and 4.03±0.07. With Phantom B, RMSEs of the 3 cm disk insert having the count density of 2 counts/pixel were 7.36±0.56, 21.21±1.52, and 6.79±0.54; for 3 counts/pixel it was 5.46±0.34, 14.43±1.08, and 4.84±0.32, for χ²_N, χ²_P, and χ²_M, respectively.(View PDF for the rest of the abstract.).

[Implementation of Statistically-Based Image Reconstruction Algorithms for CT and Numerical Evaluation of Image Quality]

[Purpose] Statistically-based image reconstruction (SIR) methods that have been incorporated into commercial CT scanners have succeeded in promoting low-dose CT with high image quality in comparison with scanners using the filtered back-projection (FBP) method. Not only researchers but also medical doctors and technologists engaged in CT studies have an interest in the algorithms of the SIR methods, however, the algorithms have not been made available to users by the CT manufacturers. Kudo reviewed the fundamentals of SIR methods on the basis of the articles published by the joint research group of each manufacturer released before product development (Med Imag Tech 32: 239-248, 2014). He classified the SIR methods into true iterative reconstruction (true IR), hybrid IR, and image space denoising (ISD) methods. His review article has made a significant contribution to the CT community of users. However, the reconstructed images obtained by those methods have not been presented. Our purpose in this study is to implement the mathematical equations of three IR methods, one each of the true IR, hybrid IR and ISD methods, and evaluate their image quality.[Methods] The system matrix of IR methods used in commercial CT scanners uses a physical photon detection process based on the finite size of an X-ray focal spot, the beam width, and the X-ray detector. However, we assumed the X-ray beam was a pencil beam and the system matrix was then given by the line integral of linear attenuation coefficients because we focus on the image quality in the ideal photon detection system equations given by Kudo. Total variation (TV) was used for regularization of the true IR, hybrid IR and ISD methods. Four kinds of numerical phantoms with 256×256 pixels were used as test images. Gaussian noise of 15, 20, 25, and 30 dB was added to the projection data with 256 linear samplings and 256 views over 180°.[Results] Root mean square errors (RMSEs) of the true IR, hybrid IR, and ISD methods were 4.28-5.70, 15.87-16.47, and 16.94-17.17, respectively. RMSE of the FBP method ranged from 27.64-33.02 and that of the FBP method processed with a Gaussian filter of FWHM (full width at half maximum) of 3 pixels ranged from 8.14-17.28. The image quality of the true IR method was superior to that of the hybrid IR and ISD methods and the FBP method.[Discussion] The noise was slightly suppressed by including the variance of projection data; however, the regularization was inevitable even if the noise levels were in the range of 25-30 dB. The noise was not suppressed sufficiently by the hybrid IR and ISD methods because the noise due to the FBP image used as the initial image for these IR methods has a dominating effect in successive reconstruction or denoise processing. Mathematical equations of each IR method were easily realized by observing the intermediate images such as the regularization term of the iteration process. In addition to these equations, the reconstructed images by the SIR methods and their RMSEs presented in this study are useful in CT research.[Conclusions] The fundamental point of SIR methods is the regularization term used in minimizing the object function.

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.

A fast method to emulate an iterative POCS image reconstruction algorithm

PURPOSE

Iterative image reconstruction algorithms are commonly used to optimize an objective function, especially when the objective function is nonquadratic. Generally speaking, the iterative algorithms are computationally inefficient. This paper presents a fast algorithm that has one backprojection and no forward projection.

METHODS

This paper derives a new method to solve an optimization problem. The nonquadratic constraint, for example, an edge-preserving denoising constraint is implemented as a nonlinear filter. The algorithm is derived based on the POCS (projections onto projections onto convex sets) approach. A windowed FBP (filtered backprojection) algorithm enforces the data fidelity. An iterative procedure, divided into segments, enforces edge-enhancement denoising. Each segment performs nonlinear filtering.

RESULTS

The derived iterative algorithm is computationally efficient. It contains only one backprojection and no forward projection. Low-dose CT data are used for algorithm feasibility studies. The nonlinearity is implemented as an edge-enhancing noise-smoothing filter.

CONCLUSIONS

The patient studies results demonstrate its effectiveness in processing low-dose x ray CT data. This fast algorithm can be used to replace many iterative algorithms.

Maximum-Likelihood Expectation-Maximization Algorithm Versus Windowed Filtered Backprojection Algorithm: A Case Study

Filtered backprojection (FBP) algorithms reduce image noise by smoothing the image. Iterative algorithms reduce image noise by noise weighting and regularization. It is believed that iterative algorithms are able to reduce noise without sacrificing image resolution, and thus iterative algorithms, especially maximum-likelihood expectation maximization (MLEM), are used in nuclear medicine to replace FBP algorithms. Methods: This short paper uses counter examples to show that this belief is not true. We compare image noise variance for FBP and MLEM reconstructions having the same spatial resolution. Results: The truth is that although MLEM suppresses image noise, it does so by sacrificing image resolution as well; the performance of windowed FBP may be better than that of MLEM in our case study. Conclusion: The myth of the superiority of iterative algorithms is caused by comparing them with conventional FBP instead of with windowed FBP. However, we do not intend to generalize the comparison results to imply which algorithm is more favorable.

Joint regularization-based image reconstruction by combining data-driven tight frame and total variation for low-dose computed tomography

Since the excessive radiation dose may induce potential body lesion, the low-dose computed tomography (LDCT) is widely applied for clinical diagnosis and treatment. However, the dose reduction will inevitably cause severe noise and degrade image quality. Most state-of-the-art methods utilize a pre-determined regularizer to account for the prior images, which may be insufficient for the most images acquired in the clinical practice. This study proposed and investigated a joint regularization method combining a data-driven tight frame and total variation (DDTF-TV) to solve this problem. Unlike the existing methods that designed pre-determined sparse transform for image domain, data-driven regularizer introduced a learning strategy to adaptively and iteratively update the framelets of DDTF, which can preferably recover the detailed image structures. The other regularizer, TV term can reconstruct strong edges and suppress noise. The joint term, DDTF-TV, collaboratively affect detail preservation and noise suppression. The proposed new model was efficiently solved by alternating the direction method of the multipliers. Qualitative and quantitative evaluations were carried out in simulation and real data experiments to demonstrate superiority of the proposed DDTF-TV method. Both visual inspection and numerical accuracy analysis show the potential of the proposed method for improving image quality of the LDCT.

Three novel accurate pixel-driven projection methods for 2D CT and 3D EPR imaging

OBJECTIVES

This work aims to explore more accurate pixel-driven projection methods for iterative image reconstructions in order to reduce high-frequency artifacts in the generated projection image.

METHODS

Three new pixel-driven projection methods namely, small-pixel-large-detector (SPLD), linear interpolation based (LIB) and distance anterpolation based (DAB), were proposed and applied to reconstruct images. The performance of these methods was evaluated in both two-dimensional (2D) computed tomography (CT) images via the modified FORBILD phantom and three-dimensional (3D) electron paramagnetic resonance (EPR) images via the 6-spheres phantom. Specifically, two evaluations based on projection generation and image reconstruction were performed. For projection generation, evaluation was using a 2D disc phantom, the modified FORBILD phantom and the 6-spheres phantom. For image reconstruction, evaluations were performed using the FORBILD and 6-spheres phantom. During evaluation, 2 quantitative indices of root-mean-square-error (RMSE) and contrast-to-noise-ratio (CNR) were used.

RESULTS

Comparing to the use of ordinary pixel-driven projection method, RMSE of the SPLD based least-square algorithm was reduced from 0.0701 to 0.0384 and CNR was increased from 5.6 to 19.47 for 2D FORBILD phantom reconstruction. For 3D EPRI, RMSE of SPLD was also reduced from 0.0594 to 0.0498 and CNR was increased from 3.88 to 11.58. In addition, visual evaluation showed that images reconstructed in both 2D and 3D images suffered from high-frequency line-shape artifacts when using the ordinary pixel-driven projection method. However, using 3 new methods all suppressed the artifacts significantly and yielded more accurate reconstructions.

CONCLUSIONS

Three proposed pixel-driven projection methods achieved more accurate iterative image reconstruction results. These new and more accurate methods can also be easily extended to other imaging modalities. Among them, SPLD method should be recommended to 3D and four dimensional (4D) EPR imaging.

Segmented separable footprint projector for digital breast tomosynthesis and its application for subpixel reconstruction

PURPOSE

Digital forward and back projectors play a significant role in iterative image reconstruction. The accuracy of the projector affects the quality of the reconstructed images. Digital breast tomosynthesis (DBT) often uses the ray-tracing (RT) projector that ignores finite detector element size. This paper proposes a modified version of the separable footprint (SF) projector, called the segmented separable footprint (SG) projector, that calculates efficiently the Radon transform mean value over each detector element. The SG projector is specifically designed for DBT reconstruction because of the large height-to-width ratio of the voxels generally used in DBT. This study evaluates the effectiveness of the SG projector in reducing projection error and improving DBT reconstruction quality.

METHODS

We quantitatively compared the projection error of the RT and the SG projector at different locations and their performance in regular and subpixel DBT reconstruction. Subpixel reconstructions used finer voxels in the imaged volume than the detector pixel size. Subpixel reconstruction with RT projector uses interpolated projection views as input to provide adequate coverage of the finer voxel grid with the traced rays. Subpixel reconstruction with the SG projector, however, uses the measured projection views without interpolation. We simulated DBT projections of a test phantom using CatSim (GE Global Research, Niskayuna, NY) under idealized imaging conditions without noise and blur, to analyze the effects of the projectors and subpixel reconstruction without other image degrading factors. The phantom contained an array of horizontal and vertical line pair patterns (1 to 9.5 line pairs/mm) and pairs of closely spaced spheres (diameters 0.053 to 0.5 mm) embedded at the mid-plane of a 5-cm-thick breast tissue-equivalent uniform volume. The images were reconstructed with regular simultaneous algebraic reconstruction technique (SART) and subpixel SART using different projectors. The resolution and contrast of the test objects in the reconstructed images and the computation times were compared under different reconstruction conditions.

RESULTS

The SG projector reduced the projector error by 1 to 2 orders of magnitude at most locations. In the worst case, the SG projector still reduced the projection error by about 50%. In the DBT reconstructed slices parallel to the detector plane, the SG projector not only increased the contrast of the line pairs and spheres but also produced more smooth and continuous reconstructed images, whereas the discrete and sparse nature of the RT projector caused artifacts appearing as patterned noise. For subpixel reconstruction, the SG projector significantly increased object contrast and computation speed, especially for high subpixel ratios, compared with the RT projector implemented with accelerated Siddon's algorithm. The difference in the depth resolution among the projectors is negligible under the conditions studied. Our results also demonstrated that subpixel reconstruction can improve the spatial resolution of the reconstructed images, and can exceed the Nyquist limit of the detector under some conditions.

CONCLUSIONS

The SG projector was more accurate and faster than the RT projector. The SG projector also substantially reduced computation time and improved the image quality for the tomosynthesized images with and without subpixel reconstruction.

Joint MR-PET Reconstruction Using a Multi-Channel Image Regularizer

While current state of the art MR-PET scanners enable simultaneous MR and PET measurements, the acquired data sets are still usually reconstructed separately. We propose a new multi-modality reconstruction framework using second order Total Generalized Variation (TGV) as a dedicated multi-channel regularization functional that jointly reconstructs images from both modalities. In this way, information about the underlying anatomy is shared during the image reconstruction process while unique differences are preserved. Results from numerical simulations and in-vivo experiments using a range of accelerated MR acquisitions and different MR image contrasts demonstrate improved PET image quality, resolution, and quantitative accuracy.

A two-step filtering-based iterative image reconstruction method for interior tomography

The optimization-based method that utilizes the additional sparse prior of region-of-interest (ROI) image, such as total variation, has been the subject of considerable research in problems of interior tomography reconstruction. One challenge for optimization-based iterative ROI image reconstruction is to build the relationship between ROI image and truncated projection data. When the reconstruction support region is smaller than the original object, an unsuitable representation of data fidelity may lead to bright truncation artifacts in the boundary region of field of view. In this work, we aim to develop an iterative reconstruction method to suppress the truncation artifacts and improve the image quality for direct ROI image reconstruction. A novel reconstruction approach is proposed based on an optimization problem involving a two-step filtering-based data fidelity. Data filtering is achieved in two steps: the first takes the derivative of projection data; in the second step, Hilbert filtering is applied in the differentiated data. Numerical simulations and real data reconstructions have been conducted to validate the new reconstruction method. Both qualitative and quantitative results indicate that, as theoretically expected, the proposed method brings reasonable performance in suppressing truncation artifacts and preserving detailed features. The presented local reconstruction method based on the two-step filtering strategy provides a simple and efficient approach for the iterative reconstruction from truncated projections.

Mixed Confidence Estimation for Iterative CT Reconstruction

Dynamic (4D) CT imaging is used in a variety of applications, but the two major drawbacks of the technique are its increased radiation dose and longer reconstruction time. Here we present a statistical analysis of our previously proposed Mixed Confidence Estimation (MCE) method that addresses both these issues. This method, where framed iterative reconstruction is only performed on the dynamic regions of each frame while static regions are fixed across frames to a composite image, was proposed to reduce computation time. In this work, we generalize the previous method to describe any application where a portion of the image is known with higher confidence (static, composite, lower-frequency content, etc.) and a portion of the image is known with lower confidence (dynamic, targeted, etc). We show that by splitting the image space into higher and lower confidence components, MCE can lower the estimator variance in both regions compared to conventional reconstruction. We present a theoretical argument for this reduction in estimator variance and verify this argument with proof-of-principle simulations. We also propose a fast approximation of the variance of images reconstructed with MCE and confirm that this approximation is accurate compared to analytic calculations of and multi-realization image variance. This MCE method requires less computation time and provides reduced image variance for imaging scenarios where portions of the image are known with more certainty than others allowing for potentially reduced radiation dose and/or improved dynamic imaging.

Volumetric CT with sparse detector arrays (and application to Si-strip photon counters)

Novel x-ray medical imaging sensors, such as photon counting detectors (PCDs) and large area CCD and CMOS cameras can involve irregular and/or sparse sampling of the detector plane. Application of such detectors to CT involves undersampling that is markedly different from the commonly considered case of sparse angular sampling. This work investigates volumetric sampling in CT systems incorporating sparsely sampled detectors with axial and helical scan orbits and evaluates performance of model-based image reconstruction (MBIR) with spatially varying regularization in mitigating artifacts due to sparse detector sampling. Volumetric metrics of sampling density and uniformity were introduced. Penalized-likelihood MBIR with a spatially varying penalty that homogenized resolution by accounting for variations in local sampling density (i.e. detector gaps) was evaluated. The proposed methodology was tested in simulations and on an imaging bench based on a Si-strip PCD (total area 5 cm  ×  25 cm) consisting of an arrangement of line sensors separated by gaps of up to 2.5 mm. The bench was equipped with translation/rotation stages allowing a variety of scanning trajectories, ranging from a simple axial acquisition to helical scans with variable pitch. Statistical (spherical clutter) and anthropomorphic (hand) phantoms were considered. Image quality was compared to that obtained with a conventional uniform penalty in terms of structural similarity index (SSIM), image uniformity, spatial resolution, contrast, and noise. Scan trajectories with intermediate helical width (~10 mm longitudinal distance per 360° rotation) demonstrated optimal tradeoff between the average sampling density and the homogeneity of sampling throughout the volume. For a scan trajectory with 10.8 mm helical width, the spatially varying penalty resulted in significant visual reduction of sampling artifacts, confirmed by a 10% reduction in minimum SSIM (from 0.88 to 0.8) and a 40% reduction in the dispersion of SSIM in the volume compared to the constant penalty (both penalties applied at optimal regularization strength). Images of the spherical clutter and wrist phantoms confirmed the advantages of the spatially varying penalty, showing a 25% improvement in image uniformity and 1.8  ×  higher CNR (at matched spatial resolution) compared to the constant penalty. The studies elucidate the relationship between sampling in the detector plane, acquisition orbit, sampling of the reconstructed volume, and the resulting image quality. They also demonstrate the benefit of spatially varying regularization in MBIR for scenarios with irregular sampling patterns. Such findings are important and integral to the incorporation of a sparsely sampled Si-strip PCD in CT imaging.

A Constrained Variable Projection Reconstruction Method for Photoacoustic Computed Tomography Without Accurate Knowledge of Transducer Responses

Photoacoustic computed tomography (PACT) is an emerging computed imaging modality that exploits optical contrast and ultrasonic detection principles to form images of the absorbed optical energy density within tissue. When the imaging system employs conventional piezoelectric ultrasonic transducers, the ideal photoacoustic (PA) signals are degraded by the transducers' acousto-electric impulse responses (EIRs) during the measurement process. If unaccounted for, this can degrade the accuracy of the reconstructed image. In principle, the effect of the EIRs on the measured PA signals can be ameliorated via deconvolution; images can be reconstructed subsequently by application of a reconstruction method that assumes an idealized EIR. Alternatively, the effect of the EIR can be incorporated into an imaging model and implicitly compensated for during reconstruction. In either case, the efficacy of the correction can be limited by errors in the assumed EIRs. In this work, a joint optimization approach to PACT image reconstruction is proposed for mitigating errors in reconstructed images that are caused by use of an inaccurate EIR. The method exploits the bi-linear nature of the imaging model and seeks to refine the measured EIR during the process of reconstructing the sought-after absorbed optical energy density. Computer-simulation and experimental studies are conducted to investigate the numerical properties of the method and demonstrate its value for mitigating image distortions and enhancing the visibility of fine structures.

Comparison of FBP and Iterative Algorithms with Non-Uniform Angular Sampling

Some people may believe that the filtered backprojection (FBP) algorithm does not work if the projection data are measured non-uniformly. Some may also believe that iterative algorithms can automatically handle the non-uniformly sampled data in the projector/backprojector. This paper claims that the FBP algorithm can effectively handle the situation where the angular sampling is not uniform. This paper compares the images that are reconstructed by both the FBP and the iterative Landweber algorithms when the angular sampling is nonuniform. When the iteration number is low, the iterative algorithms do not handle the non-uniform sampling properly. A weighting strategy is then suggested and it makes the image resolution more isotropic. In few-view tomography, the FBP and iterative algorithms both perform poorly if no other prior information is used. We have made the following observations: 1) When using an iterative algorithm, one must use early solutions due to noise amplification. 2) An early solution can have anisotropic spatial resolution if the angular sampling is not uniform. 3) The anisotropic resolution problem can be solved by introducing angle dependent weighting, which is not noise dependent. 4) The weighting is not effective when the iteration number is large. The weighting only affects the early solutions, and does not affect the converged solution. 5) When the iteration number is large, the model-mismatch errors are amplified and cause artifacts in the image. 6) The FBP algorithm is not sensitive to the model-mismatch errors, and does not have the "early solution" problems. 7) In few-view tomography, both FBP and iterative algorithms perform poorly, while the FBP algorithm gives a sharper image than the iterative algorithm does.

Analysis of iterative region-of-interest image reconstruction for x-ray computed tomography

One of the challenges for iterative image reconstruction (IIR) is that such algorithms solve an imaging model implicitly, requiring a complete representation of the scanned subject within the viewing domain of the scanner. This requirement can place a prohibitively high computational burden for IIR applied to x-ray computed tomography (CT), especially when high-resolution tomographic volumes are required. In this work, we aim to develop an IIR algorithm for direct region-of-interest (ROI) image reconstruction. The proposed class of IIR algorithms is based on an optimization problem that incorporates a data fidelity term, which compares a derivative of the estimated data with the available projection data. In order to characterize this optimization problem, we apply it to computer-simulated two-dimensional fan-beam CT data, using both ideal noiseless data and realistic data containing a level of noise comparable to that of the breast CT application. The proposed method is demonstrated for both complete field-of-view and ROI imaging. To demonstrate the potential utility of the proposed ROI imaging method, it is applied to actual CT scanner data.

Discrete imaging models for three-dimensional optoacoustic tomography using radially symmetric expansion functions

Optoacoustic tomography (OAT), also known as photoacoustic tomography, is an emerging computed biomedical imaging modality that exploits optical contrast and ultrasonic detection principles. Iterative image reconstruction algorithms that are based on discrete imaging models are actively being developed for OAT due to their ability to improve image quality by incorporating accurate models of the imaging physics, instrument response, and measurement noise. In this work, we investigate the use of discrete imaging models based on Kaiser-Bessel window functions for iterative image reconstruction in OAT. A closed-form expression for the pressure produced by a Kaiser-Bessel function is calculated, which facilitates accurate computation of the system matrix. Computer-simulation and experimental studies are employed to demonstrate the potential advantages of Kaiser-Bessel function-based iterative image reconstruction in OAT.

Full-wave iterative image reconstruction in photoacoustic tomography with acoustically inhomogeneous media

Existing approaches to image reconstruction in photoacoustic computed tomography (PACT) with acoustically heterogeneous media are limited to weakly varying media, are computationally burdensome, and/or cannot effectively mitigate the effects of measurement data incompleteness and noise. In this work, we develop and investigate a discrete imaging model for PACT that is based on the exact photoacoustic (PA) wave equation and facilitates the circumvention of these limitations. A key contribution of the work is the establishment of a procedure to implement a matched forward and backprojection operator pair associated with the discrete imaging model, which permits application of a wide-range of modern image reconstruction algorithms that can mitigate the effects of data incompleteness and noise. The forward and backprojection operators are based on the k-space pseudospectral method for computing numerical solutions to the PA wave equation in the time domain. The developed reconstruction methodology is investigated by use of both computer-simulated and experimental PACT measurement data.

First-order convex feasibility algorithms for x-ray CT

PURPOSE

Iterative image reconstruction (IIR) algorithms in computed tomography (CT) are based on algorithms for solving a particular optimization problem. Design of the IIR algorithm, therefore, is aided by knowledge of the solution to the optimization problem on which it is based. Often times, however, it is impractical to achieve accurate solution to the optimization of interest, which complicates design of IIR algorithms. This issue is particularly acute for CT with a limited angular-range scan, which leads to poorly conditioned system matrices and difficult to solve optimization problems. In this paper, we develop IIR algorithms which solve a certain type of optimization called convex feasibility. The convex feasibility approach can provide alternatives to unconstrained optimization approaches and at the same time allow for rapidly convergent algorithms for their solution-thereby facilitating the IIR algorithm design process.

METHODS

An accelerated version of the Chambolle-Pock (CP) algorithm is adapted to various convex feasibility problems of potential interest to IIR in CT. One of the proposed problems is seen to be equivalent to least-squares minimization, and two other problems provide alternatives to penalized, least-squares minimization.

RESULTS

The accelerated CP algorithms are demonstrated on a simulation of circular fan-beam CT with a limited scanning arc of 144°. The CP algorithms are seen in the empirical results to converge to the solution of their respective convex feasibility problems.

CONCLUSIONS

Formulation of convex feasibility problems can provide a useful alternative to unconstrained optimization when designing IIR algorithms for CT. The approach is amenable to recent methods for accelerating first-order algorithms which may be particularly useful for CT with limited angular-range scanning. The present paper demonstrates the methodology, and future work will illustrate its utility in actual CT application.

Forward-Projection Architecture for Fast Iterative Image Reconstruction in X-ray CT

Iterative image reconstruction can dramatically improve the image quality in X-ray computed tomography (CT), but the computation involves iterative steps of 3D forward- and back-projection, which impedes routine clinical use. To accelerate forward-projection, we analyze the CT geometry to identify the intrinsic parallelism and data access sequence for a highly parallel hardware architecture. To improve the efficiency of this architecture, we propose a water-filling buffer to remove pipeline stalls, and an out-of-order sectored processing to reduce the off-chip memory access by up to three orders of magnitude. We make a floating-point to fixed-point conversion based on numerical simulations and demonstrate comparable image quality at a much lower implementation cost. As a proof of concept, a 5-stage fully pipelined, 55-way parallel separable-footprint forward-projector is prototyped on a Xilinx Virtex-5 FPGA for a throughput of 925.8 million voxel projections/s at 200 MHz clock frequency, 4.6 times higher than an optimized 16-threaded program running on an 8-core 2.8-GHz CPU. A similar architecture can be applied to back-projection for a complete iterative image reconstruction system. The proposed algorithm and architecture can also be applied to hardware platforms such as graphics processing unit and digital signal processor to achieve significant accelerations.

A maximum NEC criterion for Compton collimation to accurately identify true coincidences in PET

In this work, we propose a new method to increase the accuracy of identifying true coincidence events for positron emission tomography (PET). This approach requires 3-D detectors with the ability to position each photon interaction in multi-interaction photon events. When multiple interactions occur in the detector, the incident direction of the photon can be estimated using the Compton scatter kinematics (Compton Collimation). If the difference between the estimated incident direction of the photon relative to a second, coincident photon lies within a certain angular range around colinearity, the line of response between the two photons is identified as a true coincidence and used for image reconstruction. We present an algorithm for choosing the incident photon direction window threshold that maximizes the noise equivalent counts of the PET system. For simulated data, the direction window removed 56%-67% of random coincidences while retaining > 94% of true coincidences from image reconstruction as well as accurately extracted 70% of true coincidences from multiple coincidences.

A residual correction method for high-resolution PET reconstruction with application to on-the-fly Monte Carlo based model of positron range

PURPOSE

The quality of tomographic images is directly affected by the system model being used in image reconstruction. An accurate system matrix is desirable for high-resolution image reconstruction, but it often leads to high computation cost. In this work the authors present a maximum a posteriori reconstruction algorithm with residual correction to alleviate the tradeoff between the model accuracy and the computation efficiency in image reconstruction.

METHODS

Unlike conventional iterative methods that assume that the system matrix is accurate, the proposed method reconstructs an image with a simplified system matrix and then removes the reconstruction artifacts through residual correction. Since the time-consuming forward and back projection operations using the accurate system matrix are not required in every iteration, image reconstruction time can be greatly reduced.

RESULTS

The authors apply the new algorithm to high-resolution positron emission tomography reconstruction with an on-the-fly Monte Carlo (MC) based positron range model. Computer simulations show that the new method is an order of magnitude faster than the traditional MC-based method, whereas the visual quality and quantitative accuracy of the reconstructed images are much better than that obtained by using the simplified system matrix alone.

CONCLUSIONS

The residual correction method can reconstruct high-resolution images and is computationally efficient.

Fast, accurate and shift-varying line projections for iterative reconstruction using the GPU

List-mode processing provides an efficient way to deal with sparse projections in iterative image reconstruction for emission tomography. An issue often reported is the tremendous amount of computation required by such algorithm. Each recorded event requires several back- and forward line projections. We investigated the use of the programmable graphics processing unit (GPU) to accelerate the line-projection operations and implement fully-3D list-mode ordered-subsets expectation-maximization for positron emission tomography (PET). We designed a reconstruction approach that incorporates resolution kernels, which model the spatially-varying physical processes associated with photon emission, transport and detection. Our development is particularly suitable for applications where the projection data is sparse, such as high-resolution, dynamic, and time-of-flight PET reconstruction. The GPU approach runs more than 50 times faster than an equivalent CPU implementation while image quality and accuracy are virtually identical. This paper describes in details how the GPU can be used to accelerate the line projection operations, even when the lines-of-response have arbitrary endpoint locations and shift-varying resolution kernels are used. A quantitative evaluation is included to validate the correctness of this new approach.