Simultaneous Algebraic Reconstruction Research Articles

Simultaneous motion estimation and image reconstruction (SMEIR) for 4D cone‐beam CT

Image reconstruction and motion model estimation in four-dimensional cone-beam CT (4D-CBCT) are conventionally handled as two sequential steps. Due to the limited number of projections at each phase, the image quality of 4D-CBCT is degraded by view aliasing artifacts, and the accuracy of subsequent motion modeling is decreased by the inferior 4D-CBCT. The objective of this work is to enhance both the image quality of 4D-CBCT and the accuracy of motion model estimation with a novel strategy enabling simultaneous motion estimation and image reconstruction (SMEIR). The proposed SMEIR algorithm consists of two alternating steps: (1) model-based iterative image reconstruction to obtain a motion-compensated primary CBCT (m-pCBCT) and (2) motion model estimation to obtain an optimal set of deformation vector fields (DVFs) between the m-pCBCT and other 4D-CBCT phases. The motion-compensated image reconstruction is based on the simultaneous algebraic reconstruction technique (SART) coupled with total variation minimization. During the forward- and backprojection of SART, measured projections from an entire set of 4D-CBCT are used for reconstruction of the m-pCBCT by utilizing the updated DVF. The DVF is estimated by matching the forward projection of the deformed m-pCBCT and measured projections of other phases of 4D-CBCT. The performance of the SMEIR algorithm is quantitatively evaluated on a 4D NCAT phantom. The quality of reconstructed 4D images and the accuracy of tumor motion trajectory are assessed by comparing with those resulting from conventional sequential 4D-CBCT reconstructions (FDK and total variation minimization) and motion estimation (demons algorithm). The performance of the SMEIR algorithm is further evaluated by reconstructing a lung cancer patient 4D-CBCT. Image quality of 4D-CBCT is greatly improved by the SMEIR algorithm in both phantom and patient studies. When all projections are used to reconstruct a 3D-CBCT by FDK, motion-blurring artifacts are present, leading to a 24.4% relative reconstruction error in the NACT phantom. View aliasing artifacts are present in 4D-CBCT reconstructed by FDK from 20 projections, with a relative error of 32.1%. When total variation minimization is used to reconstruct 4D-CBCT, the relative error is 18.9%. Image quality of 4D-CBCT is substantially improved by using the SMEIR algorithm and relative error is reduced to 7.6%. The maximum error (MaxE) of tumor motion determined from the DVF obtained by demons registration on a FDK-reconstructed 4D-CBCT is 3.0, 2.3, and 7.1 mm along left-right (L-R), anterior-posterior (A-P), and superior-inferior (S-I) directions, respectively. From the DVF obtained by demons registration on 4D-CBCT reconstructed by total variation minimization, the MaxE of tumor motion is reduced to 1.5, 0.5, and 5.5 mm along L-R, A-P, and S-I directions. From the DVF estimated by SMEIR algorithm, the MaxE of tumor motion is further reduced to 0.8, 0.4, and 1.5 mm along L-R, A-P, and S-I directions, respectively. The proposed SMEIR algorithm is able to estimate a motion model and reconstruct motion-compensated 4D-CBCT. The SMEIR algorithm improves image reconstruction accuracy of 4D-CBCT and tumor motion trajectory estimation accuracy as compared to conventional sequential 4D-CBCT reconstruction and motion estimation.

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

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. 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. 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. 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.

Improved total variation-based image reconstruction algorithm for linear scan cone-beam computed tomography

Linear scan cone-beam computed tomography (LSCBCT) is a technically simple computed tomography (CT) configuration and is powerful enough to inspect long objects. As one kind of limited-angle problem, the image reconstruction of LSCBCT is ill posed. However, the total variation minimization (TVM)-projection on convex sets (POCS) reconstruction algorithm, which is based on the TVM and POCS, has been proven effective for solving the limited-angle problem. While applying the TVM-POCS algorithm to the LSCBCT reconstruction, the reconstructed image is distorted near the edges of the object. To solve this problem, an improved iterative reconstruction algorithm was developed. The improved method integrated simultaneous algebraic reconstruction technique, TVM, and C-V model. The C-V model can detect objects whose boundaries are not necessarily defined by gradient. The developed algorithm can reduce artifacts by piecewise constant modification and get a more accurate image. Numerical simulations are presented to illustrate the effectiveness of the algorithm. Moreover, the developed algorithm can be applied to other x-ray CT reconstruction problems.

A complex image reconstruction algorithm for real-time measurement of transient field

Optical CT is now expanding into reconstruction from few views or limited-view range projection considering the economy and practicality. To solve the conflict of velocity and precision, which are two main aims that image reconstruction algorithm pursued, an innovative complex image reconstruction algorithm for real-time measurement of transient field is proposed. This method reconstructs computerized tomography (CT) image firstly by frequency spectrum approach reconstruction technique (FSART) and then by modified simultaneous algebraic reconstruction technique (MSART) and can give a fast and precise reconstruction to complicated transient field.

Nonlinear auto-adjusting iterative reconstruction technique for interferometric tomography

A new algebraic reconstruction technique (ART), nonlinear auto-adjusting iterative reconstruction technique (NAIRT), is proposed and applied to reconstruct a section of an actual thermal air flow field. With numerical simulation, NAIRT was tested to reconstruct a complicated field to demonstrate its superior reconstructive capability. In contrast, three typical ARTs, the basic ART, simultaneous ART (SART), and a modified SART (MSART), were simulated to demonstrate the reconstructive capability improvement attained through the use of the proposed NAIRT. The calculated results were discussed with mean square error (MSE) and peak error (PE). A thermal air flow field was produced with an alcohol burner and was detected by a laser beam. With laser beam projections, a cross-section of the field was reconstructed by NAIRT. As a result, the reconstructive capability was improved much by NAIRT. The MSE decreased by 95.5%, and PE by 97.2% from that of the basic ART. Only NAIRT converged without filters while its reconstructive accuracy improved. By increasing the projections from 42 to 84, the accuracy of NAIRT without filters was improved significantly. NAIRT could effectively reconstruct the section of the thermal field. The proposed NAIRT needed no filter for its convergence and it had the highest reconstructive accuracy and simplest iterative expression of those analyzed.

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.

A dual-axis tilt acquisition geometry for digital musculoskeletal tomosynthesis

Digital tomosynthesis (DT) is a limited angle tomographic x-ray technique. It is an attractive low-dose alternative to computed tomography (CT) in many imaging applications. However, the DT dataset is incomplete, which leads to out-of-focus artifacts and limited axial resolution. In this paper, a novel dual-axis tilt acquisition geometry is proposed and evaluated. This geometry solves some issues in tomosynthesis with the traditional scanning geometry by scanning the object with a set of perpendicular arcs. In this geometry the acquisition in the additional perpendicular direction is done using a tiltable object supporting platform. The proposed geometry allows for capturing more singularities of the Radon transform, filling the Fourier space with more data and better approximating the Tuy–Smith conditions. In order to evaluate the proposed system, several studies have been carried out. To validate the simulation setup the performance of the traditional scanning geometry has been simulated and compared to known results from the literature. It has also been shown that the possible improvement of the image quality in the traditional geometry is limited. These limitations can be partially overcome by using the proposed dual-axis tilt geometry. The novel geometry is superior and with the same number of projections better reconstructed images can be obtained. All studies have been made using a software tomosynthesis simulator. A micro-CT reconstruction of a bone has been used as a software phantom. Simultaneous algebraic reconstruction has been used to reconstruct simulated projections. As a conclusion, acquiring data outside the standard arc allows for improving performance of musculoskeletal tomosynthesis. With the proposed dual-axis acquisition geometry a performance gain is achieved without an increase in dose and major modifications to the instrumentation of existing tomosynthesis devices.

Three-dimensional reconstruction of flame temperature and emissivity distribution using optical tomographic and two-colour pyrometric techniques

This paper presents an experimental investigation, visualization and validation in the three-dimensional (3D) reconstruction of flame temperature and emissivity distributions by using optical tomographic and two-colour pyrometric techniques. A multi-camera digital imaging system comprising eight optical imaging fibres and two RGB charged-couple device (CCD) cameras are used to acquire two-dimensional (2D) images of the flame simultaneously from eight equiangular directions. A combined logical filtered back-projection (LFBP) and simultaneous iterative reconstruction and algebraic reconstruction technique (SART) algorithm is utilized to reconstruct the grey-level intensity of the flame for the two primary colour (red and green) images. The temperature distribution of the flame is then determined from the ratio of the reconstructed grey-level intensities and the emissivity is estimated from the ratio of the grey level of a primary colour image to that of a blackbody source at the same temperature. The temperature measurement of the system was calibrated using a blackbody furnace as a standard temperature source. Experimental work was undertaken to validate the flame temperature obtained by the imaging system against that obtained using high-precision thermocouples. The difference between the two measurements is found no greater than ±9%. Experimental results obtained on a laboratory-scale propane fired combustion test rig demonstrate that the imaging system and applied technical approach perform well in the reconstruction of the 3D temperature and emissivity distributions of the sooty flame.

SU‐E‐J‐72: Shift Invariant Feature Transform (SIFT) Based Image Stitching for Panoramic Cone Beam CT (CBCT)

Purpose: Panoramic CBCT is a novel imaging technique that stitches together projection images from multiple views to increase the imaging volume to as large as practically needed using half (200 degree gantry rotation) scans only. In this study, we investigated a SIFT‐based method to improve the accuracy of image stitching for panoramic CBCT. Methods: Panoramic CBCT data were acquired for a torso phantom using two half scans: (A) the detector at the center position and (B) the detector shifted 148mm toward the right side of the phantom. For each projection image of scan A, a corresponding projection image of the same gantry angle was interpolated for scan B using images of two neighboring gantry angles. The SIFT method was applied to extract ‘matching’ feature points in the overlapping region of the projection images of the same gantry angle from each scan. The rigid (translation and rotation) transform matrix derived from this analysis was then used to stitch together the two projection images for CBCT reconstruction using the simultaneous algebraic reconstruction technique (SART) method. Three overlapping (5‐cm, 3‐cm and 2‐cm) sizes were used for the SIFT analysis to determine the optimal imaging parameters. Results: The CBCT reconstructions using the SIFT stitching method showed significant artifact reduction compared with the direct stitching method. The success rate of matching (less than 0.5 degrees rotation and 2 pixels horizontal/vertical shifts) was close to 100% for 5‐cm overlapping and gradually reduced as the overlapping size decreased. The minimum overlapping size we could reliably apply our method was 2 cm (93.8% success rate) below which significant operator involvement was required to determine the applicable rigid transform parameters. Conclusion: We have demonstrated the effectiveness of the SIFT stitching method for panoramic CBCT reconstruction. We are currently improving the registration technique to further reduce the required overlapping size. This work was partially supported by a DOD grant DOD W81XWH1010862

SU-D-116-01: A Novel Reconstuction Framework of Prior Image Constrained Compressed Sensing (PICCS) Enabling the Use of Prior Images with Major Deviations

Purpose: To develop and investigate an improved reconstruction framework of Prior Image Constrained Compressed Sensing (PICCS) using prior images with major deviations. Methods: The novel idea of our reconstruction framework is the incorporation of a weighting matrix into the PICCS algorithm. This modification decomposes the prior image into areas that can be taken as a priori information (certain areas) and those regions that are not reliable due to motion or change in structure for the time series (uncertain areas).We applied our method to the problem of image reconstruction from few projections. Simulations were performed with the Shepp‐Logan‐Phantom considering 7 to 20 projections and different noise levels. Compared to the target image, the prior image contained major variations in shape and position of the interior structures. Objective function minimization was based on the ASD‐POCS framework using the Ordered‐Subset Simultaneous Algebraic Reconstruction Technique. For all simulations, an onboard imaging system at a linac was mimic (Source‐Detector‐Distance=1536mm, Source‐Axis‐Distance=1000mm, 512 bins detector with an overall length of 409.6mm). The size of the image array was 256×256 pixels with a resolution of 1×1mm2. The projections were generated from equidistant angles covering 196°.Image quality was quantified by the root‐mean‐squared‐error (RMSE). Results: Our method allowed accurate reconstruction of highly undersampled data. In comparison to the PICCS standard, image quality was severely improved. The increased image quality was clearly visible and is reflected in a decreased RMSE of up to 79% for noiseless and 40% for noisy projections. Conclusion: Our algorithm based on PICCS, using location dependent uncertainties of the prior image, enabled image reconstruction with increased quality even when prior images with major deviations were used. The concept indicates the potential for dose reduction while maintaining good image quality. Further development concerning registration of the prior image and real data reconstruction is currently in preparation.

TH‐C‐103‐06: Non‐Coplanar Cone Beam CT Reconstruction with Limited Angle of Projections Using Rigid Image Registration Facilitated Prior Image Constrained Compressed Sensing

Purpose: The purpose of this work is to develop a non‐coplanar cone beam CT (CBCT) image reconstruction method from limited angle of projections. Methods: Planning CT or CBCT acquired at neutral position (without couch rotation/translation) serves as the prior images for successive reconstruction. During the course of radiation therapy, subsequent CBCT scans are acquired from limited angle of projections. An iterative reconstruction algorithm, using prior image constrained compressed sensing (PICCS) framework and rigid image registration, is incorporated to reconstruct the patient image under non‐coplanar geometry. The prior reconstructed image is rotated/translated according to the nominal couch rotation/translation to serve as the prior input of the compressed sensing based iterative optimization. First, The PICCS framework can be solved iteratively using the total variation minimization step and the iterative image reconstruction step with simultaneous algebraic reconstruction technique (SART). Then, rigid image registration between the reconstructed image and the rotated/translated prior image is applied to further calibrate the rotation/translation of the prior image. The iterations of PICCS algorithm and rigid image registration continue until the registration results are below the predetermined threshold. The proposed reconstruction algorithm is evaluated with both digital phantom simulations and experimental data. Results: The proposed CBCT reconstruction algorithm significantly improved the image quality from projections with angular range as small as 72 degrees. It can reduce the rigid translational setup errors under from 8 mms to below 1 mm and the rigid rotational setup error from 5 degrees to below 1 degree. Compared with the original PICCS algorithm alone, the rigid registration step helps to improve the convergence of algorithm significantly. Conclusions: The proposed algorithm provides an accurate remedy for solving the problem of non‐coplanar CBCT reconstruction from limited angle of projections by taking advantage of the combination of PICCS framework and rigid image registration.

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.

TH‐C‐103‐02: Simultaneous Motion Estimation and Image Reconstruction (SMEIR) for 4D Cone‐Beam CT

Purpose: Image reconstruction and motion model estimation in four dimensional cone‐beam CT (4D‐CBCT) are handled as two sequential steps conventionally. Due to limited number of projections at each phase, the image quality of 4D‐CBCT is degraded by the view‐aliasing artifacts and the accuracy of subsequent motion modeling is compromised by inferior 4D‐CBCT. The objective of this work is to enhance the image quality of 4D‐CBCT and accuracy of motion model estimation through developing a novel strategy that is able to perform Simultaneous Motion Estimation and Image Reconstruction (SMEIR). Methods: The proposed SMEIR algorithm consists of two alternating steps: 1) model‐based iterative image reconstruction to obtain motion‐compensated CBCT (mCBCT) and 2) motion model estimation through the deformable registration of mCBCT and projections of individual phase of 4D‐CBCT. The iterative reconstruction is based on the simultaneous algebraic reconstruction (SART) technique coupled with total variation regularization. During the forward‐and back‐projection of SART, all projection data are used for the reconstruction of mCBCT by utilizing the estimated deformable vector fields (DVF). The DVF is estimated by matching the forward projection of the deformed mCBCT and projections of other phases of 4D‐CBCT. A 4D NCAT phantom is used to quantitatively evaluate the performance of SMEIR algorithm with comparison to FDK and total variation (TV) minimization algorithm. Results: When all projections are used for image reconstruction by FDK, motion blurring artifacts are presented in 3D‐CBCT, leading to 33.1% relative reconstruction error. View aliasing artifacts are presented in 4D‐CBCT reconstructed by FDK, where the relative error is 46.2%. When TV minimization is used, the relative error is 19.8%. Image quality of 4D‐CBCT is substantially improved by using the proposed SMEIR algorithm and relative error is reduced to 7.6%. Conclusion: The proposed SMEIR algorithm is able to estimate motion model and reconstruct motion‐compensated 4D‐CBCT with high accuracy.

Weld Defect Detection Using Iterative Image Reconstruction Methods

Non Destructive Evaluation (NDE) is a technique to detect the defects without affecting the intended application or the structure, which is mainly used for damage assessment and quality control. NDE is basically used for automation of defect quantification. This paper presents a method for weld defect detection using iterative method for image reconstruction. Image reconstruction is a technique of reconstructing the image of object from the radon transform of the object, where radon transform is obtained by passing an energy source through the object in various angles and collecting the projected data on a detector. Weld defects such as slag inclusion, lack of penetration, and burn through can cause serious disaster if it is undetected at the time of weld process. The system of linear equation under consideration in Computed Tomography (CT) are basically very large in size, so the direct method takes too much of computational time which makes it impractical for implementation. Cimmino's method and Simultaneous Algebraic Reconstruction Technique (SART) are iterative methodologies for image reconstruction which are best suited for solving large scale linear system where direct method fails due to very large time consumption. This paper compares the experimental results of image reconstruction of weld defect radiographic images using SART and Cimmino's method for various test images with varying number of projections.

The tomographic diagnostic of ITER neutral beam injector

The two-dimensional (2D) density distribution of a particle beam can be reconstructed using a diagnostic based on tomographic techniques, which measures the Dα light. This paper presents investigations and tests concerning the reliability of such a diagnostic, applied to the beam produced in MITICA (Megavolt ITER Injector & Concept Advancement) the full-size prototype of the neutral beam injector, which will be used for additional heating on ITER. It aims at developing the technologies to guarantee the correct operation of the injectors to be installed in ITER. The main target of the tomographic diagnostic is the measurement of the beam uniformity with sufficient contrast and spatial resolution, and of its evolution throughout the pulse duration. In particular the ITER beam uniformity is required to be within 10%, thus the error of the tomographic reconstruction has to be lower than this value. The conceptual design of the diagnostic is presented, with a description of the layout and main components. The portholes around the vessel and the geometry of the lines of sight are arranged so as to cover the whole area of the beam. A tomographic algorithm based on the simultaneous algebraic reconstruction technique (SART) is developed to reconstruct the beam intensity profile. Phantoms reproducing different experimental beam configurations are simulated and reconstructed with this technique. The role of noise in the line-integrated signals is studied and its effect on the reconstructed emission is investigated. The unsatisfactory results suggested the introduction of a regularization algorithm, to reduce the effect of the noise in the beam reconstruction. In this way, the simulated phantoms are correctly reconstructed and their 2D spatial non-uniformity is correctly estimated, up to a noise level of 10%.

A model based algorithm for perfusion estimation in interventional C‐arm CT systems

Interventional C-arm CT imaging, today, plays an important role in the diagnosis and treatment of patients. The main part of the 3D imaging techniques, currently used in interventions, are morphological imaging techniques. So far, the ability for functional or perfusion imaging is limited, e.g., only static cerebral blood volume measurement [A. S. Ahmed, Y. Deuerling-Zheng, C. M. Strother, K. A. Pulfer, M. Zellerhoff, T. Redel, K. Royalty, D. Consigny, M. J. Lindstrom, and D. B. Niemann, "Impact of intra-arterial injection parameters on arterial, capillary, and venous time-concentration curves in a ca480 nine model," AJNR Am. J. Neuroradiol. 30, 1337-1341 (2009)] is available. The sample rate of current C-arm CT systems is not fast enough yet to measure dynamic parameters like cerebral blood flow using standard Feldkamp reconstruction. The authors propose a reconstruction algorithm that models the time-dependent attenuation values of each voxel using a gamma-variate function. The method can be divided into a segmentation-based initialization and an iterative optimization step. For the initialization, a threshold-based segmentation of vessel, tissue, and nondynamic structures (e.g., bone and air) is performed on the filtered backprojection (FBP) reconstructions. For each of these regions, homogeneous time-attenuation curves are estimated to initialize all the voxels within the region. The scaling-factor is then adjusted for each voxel using the attenuation values of the static reconstructions. The second part of the algorithm is an iterative optimization of the gamma-variate parameters of each voxel, based on a simultaneous algebraic reconstruction technique. Within each iteration, a Levenberg optimization is applied to minimize the backprojected errors. The algorithm is quantitatively evaluated with simulated forward projections as well as real C-arm CT projection data. In the phantom experiments, penumbra and infarct core could be segmented with an adjusted Rand index of up to 0.95 for a noise level of 10(5) photons. Perfusion CT data sets from three patients were used to compare the iterative reconstruction approach to the interpolated FBP reconstruction using different sweep times. In their experiments, a sweep time of 4 s using iterative reconstruction would be equivalent to that using interpolated FBP with a sweep time of around 1 s. The reconstruction results of the animal study are compared to a perfusion CT acquisition, sampled with 1 frame per second. A correlation coefficient of 0.75 between the original and the reconstructed CBF-maps could be reached with the iterative approach compared to 0.56 using the interpolated FBP reconstruction. In their experiments, the quality of dynamic perfusion measurements was improved using the proposed reconstruction algorithm compared to static reconstruction followed by interpolation. It could be used to increase the temporal resolution of current C-arm CT system without hardware modification to make them feasible for dynamic perfusion measurement. Furthermore, radiation dose could be reduced using their method to increase temporal resolution than using static reconstruction with a higher sampling frequency.

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.

A diffusion-based truncated projection artifact reduction method for iterative digital breast tomosynthesis reconstruction

Digital breast tomosynthesis (DBT) has strong promise to improve sensitivity for detecting breast cancer. DBT reconstruction estimates the breast tissue attenuation using projection views (PVs) acquired in a limited angular range. Because of the limited field of view (FOV) of the detector, the PVs may not completely cover the breast in the x-ray source motion direction at large projection angles. The voxels in the imaged volume cannot be updated when they are outside the FOV, thus causing a discontinuity in intensity across the FOV boundaries in the reconstructed slices, which we refer to as the truncated projection artifact (TPA). Most existing TPA reduction methods were developed for the filtered backprojection method in the context of computed tomography. In this study, we developed a new diffusion-based method to reduce TPAs during DBT reconstruction using the simultaneous algebraic reconstruction technique (SART). Our TPA reduction method compensates for the discontinuity in background intensity outside the FOV of the current PV after each PV updating in SART. The difference in voxel values across the FOV boundary is smoothly diffused to the region beyond the FOV of the current PV. Diffusion-based background intensity estimation is performed iteratively to avoid structured artifacts. The method is applicable to TPA in both the forward and backward directions of the PVs and for any number of iterations during reconstruction. The effectiveness of the new method was evaluated by comparing the visual quality of the reconstructed slices and the measured discontinuities across the TPA with and without artifact correction at various iterations. The results demonstrated that the diffusion-based intensity compensation method reduced the TPA while preserving the detailed tissue structures. The visibility of breast lesions obscured by the TPA was improved after artifact reduction.

Convergence analysis of SART: optimization and statistics

Simultaneous algebraic reconstruction technique (SART) [A. Andersen, Algebraic reconstruction in CT from limited views, IEEE Trans. Med. Imaging 8 (1989), pp. 50–55; A. Andersen and A. Kak, Simultaneous algebraic reconstruction technique (SART): A superior implementation of the ART algorithm, Ultrason. Imaging 6 (1984), pp. 81–94] is an iterative method for solving inverse problems of form Ax(+n)=b. These kinds of problems arise, for example, in computed tomography (CT) reconstruction, in which case A is obtained from the discrete Radon transform. In this paper, we provide several methods for derivation of SART and connections between SART and other methods. Using these connections, we also prove the convergence of SART in different ways. These approaches are from optimization and statistical points of view and can be applied to other Landweber-like schemes such as Cimmino's algorithm and component averaging. Furthermore, the noisy case is considered and the error estimation is given. Several numerical experiments for CT reconstruction are provided to demonstrate the convergence results in practice.

Constrained SART algorithm for inverse problems in image reconstruction

In this paper we integrate the SART (Simultaneous Algebraic Reconstruction Technique) algorithm into a general iterative method, introduced in [8]. This general method offers us the possibility of achieving a new convergence proof of the SART method and prove the convergence of the constrained version of SART. Systematic numerical experiments, comparing SART and Kaczmarz-like algorithms, are made on two phantoms widely used in image reconstruction literature.