Simultaneous Algebraic Reconstruction Technique Reconstruction Research Articles

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.

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

ContextThere has been considerable progress in the instrumentation for data measurement and computer methods for generating images of measured PET data. These computer methods have been developed to solve the inverse problem, also known as the “image reconstruction from projections” problem. AimIn this paper, we propose a modified Simultaneous Algebraic Reconstruction Technique (SART) algorithm to improve the quality of image reconstruction by incorporating total variation (TV) minimization into the iterative SART algorithm. MethodologyThe SART updates the estimated image by forward projecting the initial image onto the sinogram space. Then, the difference between the estimated sinogram and the given sinogram is back-projected onto the image domain. This difference is then subtracted from the initial image to obtain a corrected image. Fast total variation (FTV) minimization is applied to the image obtained in the SART step. The second step is the result obtained from the previous FTV update. The SART and the FTV minimization steps run iteratively in an alternating manner. Fifty iterations were applied to the SART algorithm used in each of the regularization-based methods. In addition to the conventional SART algorithm, spatial smoothing was used to enhance the quality of the image. All images were sized at 128 × 128 pixels. ResultsThe proposed algorithm successfully accomplished edge preservation. A detailed scrutiny revealed that the reconstruction algorithms differed; for example, the SART and the proposed FTV-SART algorithm effectively preserved the hot lesion edges, whereas artifacts and deviations were more likely to occur in the ART algorithm than in the other algorithms. ConclusionsCompared to the standard SART, the proposed algorithm is more robust in removing background noise while preserving edges to suppress the existent image artifacts. The quality measurements and visual inspections show a significant improvement in image quality compared to the conventional SART and Algebraic Reconstruction Technique (ART) algorithms.

Sparse-view neutron CT reconstruction of irradiated fuel assembly using total variation minimization with Poisson statistics

We inspect the nuclear fuel assembly by demonstrating the potential use of sparse-view neutron computed tomography. The projection images of the fuel assembly were collected at the Idaho National Laboratory hot fuel examination facility using indirect foil-film transfer technique. The radiographs were digitized using a commercial film digitizer and registered spatially for reconstruction. Digitized data were reconstructed using simultaneous algebraic reconstruction technique (SART) with total variation minimization using a dual approach for numerical solution assuming the projection data are corrupted by Poisson noise. To validate and evaluate the performance of the algorithm, visual inspections, as well as quantitative evaluation studies using a computer simulation data and the experimental data of the fuel assembly were carried out. The proposed method provides better reconstruction for both simulated and experimental case in terms of artifact reduction, higher SNR, and better spatial resolution compared to the reconstruction yielded by filtered back projection and SART reconstruction.

A hybrid tomographic reconstruction algorithm for high speed X-ray tomography

This paper compares two techniques for reconstructing images from time-resolved X-ray tomography data: Simultaneous Algebraic Reconstruction Technique (SART) and Adaptive Genetic Algorithm (AGA). The advantages and disadvantages of both are discussed, and we combine them into a hybrid algorithm. The hybrid method uses results from AGA as the starting values for SART. We demonstrate that this leads to improved reconstruction results: less noise than SART and better reconstruction of shapes than AGA.

Computer-aided detection of clustered microcalcifications in multiscale bilateral filtering regularized reconstructed digital breast tomosynthesis volume.

Develop a computer-aided detection (CADe) system for clustered microcalcifications in digital breast tomosynthesis (DBT) volume enhanced with multiscale bilateral filtering (MSBF) regularization. With Institutional Review Board approval and written informed consent, two-view DBT of 154 breasts, of which 116 had biopsy-proven microcalcification (MC) clusters and 38 were free of MCs, was imaged with a General Electric GEN2 prototype DBT system. The DBT volumes were reconstructed with MSBF-regularized simultaneous algebraic reconstruction technique (SART) that was designed to enhance MCs and reduce background noise while preserving the quality of other tissue structures. The contrast-to-noise ratio (CNR) of MCs was further improved with enhancement-modulated calcification response (EMCR) preprocessing, which combined multiscale Hessian response to enhance MCs by shape and bandpass filtering to remove the low-frequency structured background. MC candidates were then located in the EMCR volume using iterative thresholding and segmented by adaptive region growing. Two sets of potential MC objects, cluster centroid objects and MC seed objects, were generated and the CNR of each object was calculated. The number of candidates in each set was controlled based on the breast volume. Dynamic clustering around the centroid objects grouped the MC candidates to form clusters. Adaptive criteria were designed to reduce false positive (FP) clusters based on the size, CNR values and the number of MCs in the cluster, cluster shape, and cluster based maximum intensity projection. Free-response receiver operating characteristic (FROC) and jackknife alternative FROC (JAFROC) analyses were used to assess the performance and compare with that of a previous study. Unpaired two-tailed t-test showed a significant increase (p < 0.0001) in the ratio of CNRs for MCs with and without MSBF regularization compared to similar ratios for FPs. For view-based detection, a sensitivity of 85% was achieved at an FP rate of 2.16 per DBT volume. For case-based detection, a sensitivity of 85% was achieved at an FP rate of 0.85 per DBT volume. JAFROC analysis showed a significant improvement in the performance of the current CADe system compared to that of our previous system (p = 0.003). MBSF regularized SART reconstruction enhances MCs. The enhancement in the signals, in combination with properly designed adaptive threshold criteria, effective MC feature analysis, and false positive reduction techniques, leads to a significant improvement in the detection of clustered MCs in DBT.

Technical note: algebraic iterative image reconstruction using a cylindrical image grid for tetrahedron beam computed tomography.

To accelerate iterative algebraic reconstruction algorithms using a cylindrical image grid. Tetrahedron beam computed tomography (TBCT) is designed to overcome the scatter and detector problems of cone beam computed tomography (CBCT). Iterative algebraic reconstruction algorithms have been shown to mitigate approximate reconstruction artifacts that appear at large cone angles, but clinical implementation is limited by their high computational cost. In this study, a cylindrical voxelization method on a cylindrical grid is developed in order to take advantage of the symmetries of the cylindrical geometry. The cylindrical geometry is a natural fit for the circular scanning trajectory employed in volumetric CT methods such as CBCT and TBCT. This method was implemented in combination with the simultaneous algebraic reconstruction technique (SART). Both two- and three-dimensional numerical phantoms as well as a patient CT image were utilized to generate the projection sets used for reconstruction. The reconstructed images were compared to the original phantoms using a set of three figures of merit (FOM). The cylindrical voxelization on a cylindrical reconstruction grid was successfully implemented in combination with the SART reconstruction algorithm. The FOM results showed that the cylindrical reconstructions were able to maintain the accuracy of the Cartesian reconstructions. In three dimensions, the cylindrical method provided better accuracy than the Cartesian methods. At the same time, the cylindrical method was able to provide a speedup factor of approximately 40 while also reducing the system matrix storage size by 2 orders of magnitude. TBCT image reconstruction using a cylindrical image grid was able to provide a significant improvement in the reconstruction time and a more compact system matrix for storage on the hard drive and in memory while maintaining the image quality provided by the Cartesian voxelization on a Cartesian grid.

TH‐C‐103‐04: Computed Tomography Image Reconstruction with a Cylindrical Voxelization Method

Purpose: To accelerate the image reconstruction process for iterative algebraic reconstruction techniques using a cylindrical voxelization method. Methods: Iterative image reconstruction has many advantages, such as noise reduction and mitigation of approximate cone reconstruction artifacts, over analytical image reconstruction. But its high computational cost prohibits its use in many clinical applications, such as image guided radiotherapy (IGRT). The system matrix used in iterative reconstruction is often too large to store on the hard drive or in RAM. The cylindrical geometry is a natural fit for the circular scanning trajectory employed in volumetric CT methods such as cone beam computed tomography (CBCT) and tetrahedron beam computed tomography (TBCT). In this study, the iterative simultaneous algebraic reconstruction technique (SART) algorithm using a cylindrical voxelization method is developed for TBCT. The new algorithm takes advantage of the symmetries of the axial scanning geometry used in TBCT and greatly reduces the size of the system matrix. An additional step is needed for interpolating the cylindrical data onto a Cartesian grid. The reconstruction algorithms were tested with numerical phantoms as well as patient CT data. Results: The system matrix with the cylindrical voxelization method is compact and can be easily stored in the computer RAM. SART reconstruction using the cylindrical voxelization method was implemented for the TBCT. The FOM results for the cylindrical voxelization method were slightly better than for the Cartesian voxelization. The cylindrical method was able to provide a speedup of 40 times over the traditional Cartesian method and to provide a reduction of two orders of magnitude in the storage requirement for the system matrix. Conclusion: Image reconstruction using a cylindrical voxelization method was able to provide a significant improvement in the reconstruction speed while maintaining the image quality provided by the conventional reconstruction method using a Cartesian image grid. This work is partially supported by NIH SBIR contract #HHSN261201100045C.

Weighted simultaneous algebraic reconstruction technique for tomosynthesis imaging of objects with high‐attenuation features

This paper introduces a nonlinear weighting scheme into the backprojection operation within the simultaneous algebraic reconstruction technique (SART). It is designed for tomosynthesis imaging of objects with high-attenuation features in order to reduce limited angle artifacts. The algorithm estimates which projections potentially produce artifacts in a voxel. The contribution of those projections into the updating term is reduced. In order to identify those projections automatically, a four-dimensional backprojected space representation is used. Weighting coefficients are calculated based on a dissimilarity measure, evaluated in this space. For each combination of an angular view direction and a voxel position an individual weighting coefficient for the updating term is calculated. The feasibility of the proposed approach is shown based on reconstructions of the following real three-dimensional tomosynthesis datasets: a mammography quality phantom, an apple with metal needles, a dried finger bone in water, and a human hand. Datasets have been acquired with a Siemens Mammomat Inspiration tomosynthesis device and reconstructed using SART with and without suggested weighting. Out-of-focus artifacts are described using line profiles and measured using standard deviation (STD) in the plane and below the plane which contains artifact-causing features. Artifacts distribution in axial direction is measured using an artifact spread function (ASF). The volumes reconstructed with the weighting scheme demonstrate the reduction of out-of-focus artifacts, lower STD (meaning reduction of artifacts), and narrower ASF compared to nonweighted SART reconstruction. It is achieved successfully for different kinds of structures: point-like structures such as phantom features, long structures such as metal needles, and fine structures such as trabecular bone structures. Results indicate the feasibility of the proposed algorithm to reduce typical tomosynthesis artifacts produced by high-attenuation features. The proposed algorithm assigns weighting coefficients automatically and no segmentation or tissue-classification steps are required. The algorithm can be included into various iterative reconstruction algorithms with an additive updating strategy. It can also be extended to computed tomography case with the complete set of angular data.

TH‐C‐BRA‐03: Fast Iterative Cone Beam CT Reconstruction on GPGPU Using OpenCL

Purpose: Algebraic reconstruction technique (ART) type algorithms produce superior image quality for CBCT and CT reconstructions over the popular filtered‐back‐projection based approaches but are too slow for real‐time clinical applications. The purpose of this study is to employ the emerging OpenCL architecture to accelerate simultaneous ART (SART) by parallelizing the most time‐consuming forward‐ and back‐projections using General‐Purpose‐Graphics‐Processing‐Unit (GPGPU). Methods: For each iteration, SART sequentially performs three ray‐driven projections (one forward‐ and two back‐projections) for each acquired projection image. To accelerate SART reconstruction, both forward projection and back‐projection kernels were scheduled on GPGPU using data parallelism to take full advantage of compute units on GPGPU. The single‐work‐item‐for‐single‐ray technique was employed as parallelization mechanism. We conducted numerical experiments to test OpenCL‐based implementation on a Dell Precision T7500 workstation with two quad‐core CPUs and one Nvidia Tesla C2050 GPGPU. Poly‐energetic projection data (512×512) for the Mohan 4 MV energy spectrum were simulated each degree for 360 gantry angles for a head‐and‐neck digital phantom and were fed into the SART algorithms for CBCT reconstruction of 256×256×256 volume. To accelerate poly‐energetic projection computation, we partitioned the workloads using task parallelism and data parallelism and scheduled them in a parallel computing ecosystem consisting of CPU and GPGPU using OpenCL only. Results: The GPGPU computation time including the kernel launch time, kernel running time and data transfer time was 42 ms for forward‐projection and 95 ms for back‐projection. Each SART iteration took 101 s on GPGPU in comparison to 7195 s on a single‐threaded CPU. The proposed method achieved a ∼71 ‐times speedup. The relative difference of the reconstructed images between the CPU‐based and OpenCL/GPGPU‐based implementations was on the order of 0.00001 and virtually indistinguishable. Conclusions: We have successfully implemented the SART algorithm on GPGPU using OpenCL and significantly reduced the reconstruction time to a level that is almost suitable for real‐time clinical applications.

Selective‐diffusion regularization for enhancement of microcalcifications in digital breast tomosynthesis reconstruction

Digital breast tomosynthesis (DBT) has been shown to improve mass detection. Detection of microcalcifications is more challenging because of the large breast volume to be searched for subtle signals. The simultaneous algebraic reconstruction technique (SART) was found to provide good image quality for DBT, but the image noise is amplified with an increasing number of iterations. In this study, the authors developed a selective-diffusion (SD) method for noise regularization with SART to improve the contrast-to-noise ratio (CNR) of microcalcifications in the DBT slices for human or machine detection. The SD method regularizes SART reconstruction during updating with each projection view. Potential microcalcifications are differentiated from the noisy background by estimating the local gradient information. Different degrees of regularization are applied to the signal or noise classes, such that the microcalcifications will be enhanced while the noise is suppressed. The new SD method was compared to several current methods, including the quadratic Laplacian (QL) method, the total variation (TV) method, and the nonconvex total p-variation (TpV) method for noise regularization with SART. A GE GEN2 prototype DBT system with a stationary digital detector was used for the acquisition of DBT scans at 21 angles in 3 degrees increments over a +/-30 degrees range. The reconstruction image quality without regularization and that with the different regularization methods were compared using the DBT scans of an American College of Radiology phantom and a human subject. The CNR and the full width at half maximum (FWHM) of the line profiles of microcalcifications within the in-focus DBT slices were used as image quality measures. For the comparison of large microcalcifications in the DBT data of the subject, the SD method resulted in comparable CNR to the nonconvex TpV method. Both of them performed better than the other two methods. For subtle microcalcifications, the SD method was superior to other methods in terms of CNR. In both the subject and phantom DBT data, for large microcalcifications, the FWHM of the SD method was comparable to that without regularization, which was wider than that of the TV type methods. For subtle microcalcifications, the SD method had comparable FWHM values to the TV type methods. All three regularization methods were superior to the QL method in terms of FWHM. The SART regularized by the selective-diffusion method enhanced the CNR and preserved the sharpness of microcalcifications. In comparison with three existing regularization methods, the selective-diffusion regularization was superior to the other methods for subtle microcalcifications.

Application of boundary detection information in breast tomosynthesis reconstruction.

Digital tomosynthesis mammography (DTM) is one of the most promising techniques that can potentially improve early detection of breast cancers. DTM can provide three-dimensional (3D) structural information by reconstructing the whole imaged volume from a sequence of projection-view (PV) mammograms that are acquired at a small number of projection angles over a limited angular range. Our previous study showed that simultaneous algebraic reconstruction technique (SART) can produce satisfactory tomosynthesized image quality compared to maximum likelihood-type algorithms. To improve the efficiency of DTM reconstruction and address the problem of boundary artifacts, we have developed methods to incorporate both two-dimensional (2D) and 3D breast boundary information within the SART reconstruction algorithm in this study. A second generation GE prototype tomosynthesis mammography system with a stationary digital detector was used for PV image acquisition from 21 angles in 3 degrees increments over a +/- 30 degrees angular range. The 2D breast boundary curves on all PV images were obtained by automated segmentation and were used to restrict the SART reconstruction to be performed only within the breast volume. The computation time of SART reconstruction was reduced by 76.3% and 69.9% for cranio-caudal and mediolateral oblique views, respectively, for the chosen example. In addition, a 3D conical trimming method was developed in which the 2D breast boundary curves from all PVs were back projected to generate the 3D breast surface. This 3D surface was then used to eliminate the multiple breast shadows outside the breast volume due to reconstruction by setting these voxels to a constant background value. Our study demonstrates that, by using the 2D and 3D breast boundary information, all breast boundary and most detector boundary artifacts can be effectively removed on all tomosynthesized slices.