L Zhu

Compressed sensing based cone-beam computed tomography reconstruction with a first-order method

PURPOSE This article considers the problem of reconstructing cone-beam computed tomography (CBCT) images from a set of undersampled and potentially noisy projection measurements. METHODS The authors cast the reconstruction as a compressed sensing problem based onℓ1 norm minimization constrained by statistically weighted least-squares of CBCT projection data. For accurate modeling, the noise characteristics of the CBCT projection data are used to determine the relative importance of each projection measurement. To solve the compressed sensing problem, the authors employ a method minimizing total-variation norm, satisfying a prespecified level of measurement consistency using a first-order method developed by Nesterov. RESULTS The method converges fast to the optimal solution without excessive memory requirement, thanks to the method of iterative forward and back-projections. The performance of the proposed algorithm is demonstrated through a series of digital and experimental phantom studies. It is found a that high quality CBCT image can be reconstructed from undersampled and potentially noisy projection data by using the proposed method. Both sparse sampling and decreasing x-ray tube current (i.e., noisy projection data) lead to the reduction of radiation dose in CBCT imaging. CONCLUSIONS It is demonstrated that compressed sensing outperforms the traditional algorithm when dealing with sparse, and potentially noisy, CBCT projection views.

Scatter correction for full‐fan volumetric CT using a stationary beam blocker in a single full scan

PURPOSE Applications of volumetric CT (VCT) are hampered by shading and streaking artifacts in the reconstructed images. These artifacts are mainly due to strong x-ray scatter signals accompanied with the large illumination area within one projection, which lead to CT number inaccuracy, image contrast loss and spatial nonuniformity. Although different scatter correction algorithms have been proposed in literature, a standard solution still remains unclear. Measurement-based methods use a beam blocker to acquire scatter samples. These techniques have unrivaled advantages over other existing algorithms in that they are simple and efficient, and achieve high scatter estimation accuracy without prior knowledge of the imaged object. Nevertheless, primary signal loss is inevitable in the scatter measurement, and multiple scans or moving the beam blocker during data acquisition are typically employed to compensate for the missing primary data. In this paper, we propose a new measurement-based scatter correction algorithm without primary compensation for full-fan VCT. An accurate reconstruction is obtained with one single-scan and a stationary x-ray beam blocker, two seemingly incompatible features which enable simple and efficient scatter correction without increase of scan time or patient dose. METHODS Based on the CT reconstruction theory, we distribute the blocked data over the projection area where primary signals are considered approximately redundant in a full scan, such that the CT image quality is not degraded even with primary loss. Scatter is then accurately estimated by interpolation and scatter-corrected CT images are obtained using an FDK-based reconstruction algorithm. RESULTS The proposed method is evaluated using two phantom studies on a tabletop CBCT system. On the Catphan©600 phantom, our approach reduces the reconstruction error from 207 Hounsfield unit (HU) to 9 HU in the selected region of interest, and improves the image contrast by a factor of 2.0 in the high-contrast regions. On an anthropomorphic head phantom, the reconstruction error is reduced from 97 HU to 6 HU in the soft tissue region and image spatial nonuniformity decreases from 27% to 5% after correction. CONCLUSIONS Our method inherits the main advantages of measurement-based methods while avoiding their shortcomings. It has the potential to become a practical scatter correction solution widely implementable on different VCT systems.

Accelerated barrier optimization compressed sensing (ABOCS) reconstruction for cone-beam CT: phantom studies.

PURPOSE Recent advances in compressed sensing (CS) enable accurate CT image reconstruction from highly undersampled and noisy projection measurements, due to the sparsifiable feature of most CT images using total variation (TV). These novel reconstruction methods have demonstrated advantages in clinical applications where radiation dose reduction is critical, such as onboard cone-beam CT (CBCT) imaging in radiation therapy. The image reconstruction using CS is formulated as either a constrained problem to minimize the TV objective within a small and fixed data fidelity error, or an unconstrained problem to minimize the data fidelity error with TV regularization. However, the conventional solutions to the above two formulations are either computationally inefficient or involved with inconsistent regularization parameter tuning, which significantly limit the clinical use of CS-based iterative reconstruction. In this paper, we propose an optimization algorithm for CS reconstruction which overcomes the above two drawbacks. METHODS The data fidelity tolerance of CS reconstruction can be well estimated based on the measured data, as most of the projection errors are from Poisson noise after effective data correction for scatter and beam-hardening effects. We therefore adopt the TV optimization framework with a data fidelity constraint. To accelerate the convergence, we first convert such a constrained optimization using a logarithmic barrier method into a form similar to that of the conventional TV regularization based reconstruction but with an automatically adjusted penalty weight. The problem is then solved efficiently by gradient projection with an adaptive Barzilai-Borwein step-size selection scheme. The proposed algorithm is referred to as accelerated barrier optimization for CS (ABOCS), and evaluated using both digital and physical phantom studies. RESULTS ABOCS directly estimates the data fidelity tolerance from the raw projection data. Therefore, as demonstrated in both digital Shepp-Logan and physical head phantom studies, consistent reconstruction performances are achieved using the same algorithm parameters on scans with different noise levels and∕or on different objects. On the contrary, the penalty weight in a TV regularization based method needs to be fine-tuned in a large range (up to seven times) to maintain the reconstructed image quality. The improvement of ABOCS on computational efficiency is demonstrated in the comparisons with adaptive-steepest-descent-projection-onto-convex-sets (ASD-POCS), an existing CS reconstruction algorithm also using constrained optimization. ASD-POCS alternatively minimizes the TV objective using adaptive steepest descent (ASD) and the data fidelity error using projection onto convex sets (POCS). For similar image qualities of the Shepp-Logan phantom, ABOCS requires less computation time than ASD-POCS in MATLAB by more than one order of magnitude. CONCLUSIONS We propose ABOCS for CBCT reconstruction. As compared to other published CS-based algorithms, our method has attractive features of fast convergence and consistent parameter settings for different datasets. These advantages have been demonstrated on phantom studies.PURPOSE Recent advances in compressed sensing (CS) enable accurate CT image reconstruction from highly undersampled and noisy projection measurements, due to the sparsifiable feature of most CT images using total variation (TV). These novel reconstruction methods have demonstrated advantages in clinical applications where radiation dose reduction is critical, such as onboard cone-beam CT (CBCT) imaging in radiation therapy. The image reconstruction using CS is formulated as either a constrained problem to minimize the TV objective within a small and fixed data fidelity error, or an unconstrained problem to minimize the data fidelity error with TV regularization. However, the conventional solutions to the above two formulations are either computationally inefficient or involved with inconsistent regularization parameter tuning, which significantly limit the clinical use of CS-based iterative reconstruction. In this paper, we propose an optimization algorithm for CS reconstruction which overcomes the above two drawbacks. METHODS The data fidelity tolerance of CS reconstruction can be well estimated based on the measured data, as most of the projection errors are from Poisson noise after effective data correction for scatter and beam-hardening effects. We therefore adopt the TV optimization framework with a data fidelity constraint. To accelerate the convergence, we first convert such a constrained optimization using a logarithmic barrier method into a form similar to that of the conventional TV regularization based reconstruction but with an automatically adjusted penalty weight. The problem is then solved efficiently by gradient projection with an adaptive Barzilai-Borwein step-size selection scheme. The proposed algorithm is referred to as accelerated barrier optimization for CS (ABOCS), and evaluated using both digital and physical phantom studies. RESULTS ABOCS directly estimates the data fidelity tolerance from the raw projection data. Therefore, as demonstrated in both digital Shepp-Logan and physical head phantom studies, consistent reconstruction performances are achieved using the same algorithm parameters on scans with different noise levels and/or on different objects. On the contrary, the penalty weight in a TV regularization based method needs to be fine-tuned in a large range (up to seven times) to maintain the reconstructed image quality. The improvement of ABOCS on computational efficiency is demonstrated in the comparisons with adaptive-steepest-descent-projection-onto-convex-sets (ASD-POCS), an existing CS reconstruction algorithm also using constrained optimization. ASD-POCS alternatively minimizes the TV objective using adaptive steepest descent (ASD) and the data fidelity error using projection onto convex sets (POCS). For similar image qualities of the Shepp-Logan phantom, ABOCS requires less computation time than ASD-POCS inMATLAB by more than one order of magnitude. CONCLUSIONS We propose ABOCS for CBCT reconstruction. As compared to other published CS-based algorithms, our method has attractive features of fast convergence and consistent parameter settings for different datasets. These advantages have been demonstrated on phantom studies.

Scatter correction method for x-ray CT using primary modulation: Phantom studies

PURPOSE Scatter correction is a major challenge in x-ray imaging using large area detectors. Recently, the authors proposed a promising scatter correction method for x-ray computed tomography (CT) using primary modulation. Proof of concept was previously illustrated by Monte Carlo simulations and physical experiments on a small phantom with a simple geometry. In this work, the authors provide a quantitative evaluation of the primary modulation technique and demonstrate its performance in applications where scatter correction is more challenging. METHODS The authors first analyze the potential errors of the estimated scatter in the primary modulation method. On two tabletop CT systems, the method is investigated using three phantoms: A Catphan 600 phantom, an anthropomorphic chest phantom, and the Catphan 600 phantom with two annuli. Two different primary modulators are also designed to show the impact of the modulator parameters on the scatter correction efficiency. The first is an aluminum modulator with a weak modulation and a low modulation frequency, and the second is a copper modulator with a strong modulation and a high modulation frequency. RESULTS On the Catphan 600 phantom in the first study, the method reduces the error of the CT number in the selected regions of interest (ROIs) from 371.4 to 21.9 Hounsfield units (HU); the contrast to noise ratio also increases from 10.9 to 19.2. On the anthropomorphic chest phantom in the second study, which represents a more difficult case due to the high scatter signals and object heterogeneity, the method reduces the error of the CT number from 327 to 19 HU in the selected ROIs and from 31.4% to 5.7% on the overall average. The third study is to investigate the impact of object size on the efficiency of our method. The scatter-to-primary ratio estimation error on the Catphan 600 phantom without any annulus (20 cm in diameter) is at the level of 0.04, it rises to 0.07 and 0.1 on the phantom with an elliptical annulus (30 cm in the minor axis and 38 cm in the major axis) and with a circular annulus (38 cm in diameter). CONCLUSIONS On the three phantom studies, good scatter correction performance of the proposed method has been demonstrated using both image comparisons and quantitative analysis. The theory and experiments demonstrate that a strong primary modulation that possesses a low transmission factor and a high modulation frequency is preferred for high scatter correction accuracy.

Three-dimensional anisotropic adaptive filtering of projection data for noise reduction in cone beam CT

PURPOSE The combination of quickly rotating C-arm gantry with digital flat panel has enabled the acquisition of three-dimensional data (3D) in the interventional suite. However, image quality is still somewhat limited since the hardware has not been optimized for CT imaging. Adaptive anisotropic filtering has the ability to improve image quality by reducing the noise level and therewith the radiation dose without introducing noticeable blurring. By applying the filtering prior to 3D reconstruction, noise-induced streak artifacts are reduced as compared to processing in the image domain. METHODS 3D anisotropic adaptive filtering was used to process an ensemble of 2D x-ray views acquired along a circular trajectory around an object. After arranging the input data into a 3D space (2D projections + angle), the orientation of structures was estimated using a set of differently oriented filters. The resulting tensor representation of local orientation was utilized to control the anisotropic filtering. Low-pass filtering is applied only along structures to maintain high spatial frequency components perpendicular to these. The evaluation of the proposed algorithm includes numerical simulations, phantom experiments, and in-vivo data which were acquired using an AXIOM Artis dTA C-arm system (Siemens AG, Healthcare Sector, Forchheim, Germany). Spatial resolution and noise levels were compared with and without adaptive filtering. A human observer study was carried out to evaluate low-contrast detectability. RESULTS The adaptive anisotropic filtering algorithm was found to significantly improve low-contrast detectability by reducing the noise level by half (reduction of the standard deviation in certain areas from 74 to 30 HU). Virtually no degradation of high contrast spatial resolution was observed in the modulation transfer function (MTF) analysis. Although the algorithm is computationally intensive, hardware acceleration using Nvidias CUDA Interface provided an 8.9-fold speed-up of the processing (from 1336 to 150 s). CONCLUSIONS Adaptive anisotropic filtering has the potential to substantially improve image quality and/or reduce the radiation dose required for obtaining 3D image data using cone beam CT.

Modulator design for x‐ray scatter correction using primary modulation: Material selection

PURPOSE An optimal material selection for primary modulator is proposed in order to minimize beam hardening of the modulator in x-ray cone-beam computed tomography (CBCT). Recently, a measurement-based scatter correction method using primary modulation has been developed and experimentally verified. In the practical implementation, beam hardening of the modulator blocker is a limiting factor because it causes inconsistency in the primary signal and therefore degrades the accuracy of scatter correction. METHODS This inconsistency can be purposely assigned to the effective transmission factor of the modulator whose variation as a function of object filtration represents the magnitude of beam hardening of the modulator. In this work, the authors show that the variation reaches a minimum when the K-edge of the modulator material is near the mean energy of the system spectrum. Accordingly, an optimal material selection can be carried out in three steps. First, estimate and evaluate the polychromatic spectrum for a given x-ray system including both source and detector; second, calculate the mean energy of the spectrum and decide the candidate materials whose K-edge energies are near the mean energy; third, select the optimal material from the candidates after considering both the magnitude of beam hardening and the physical and chemical properties. RESULTS A tabletop x-ray CBCT system operated at 120 kVp is used to validate the material selection method in both simulations and experiments, from which the optimal material for this x-ray system is then chosen. With the transmission factor initially being 0.905 and 0.818, simulations show that erbium provides the least amount of variation as a function of object filtrations (maximum variations are 2.2% and 4.3%, respectively, only one-third of that for copper). With different combinations of aluminum and copper filtrations (simulating a range of object thicknesses), measured overall variations are 2.5%, 1.0%, and 8.6% for 25.4 microm of copper, erbium, and tungsten, respectively. With and without 300 microm of copper in the beam, the measured variations for 25.4 microm of copper, erbium, and tungsten, 1 mm of aluminum, as well as 406 microm of copper, are 1.8%, 0.2%, 5.5%, 1.9%, and 7.5%, respectively. CONCLUSIONS The spatial variation in the effective transmission factor of the modulator blocker due to beam hardening caused by the modulator itself reaches a minimum when the K-edge of the modulator material is near the mean energy of the spectrum. An optimal modulator material selection using the K-edge discontinuity is therefore proposed.

Optimization of system parameters for modulator design in x-ray scatter correction using primary modulation

The impact of the system parameters of the modulator on X-ray scatter correction using primary modulation is studied and an optimization of the modulator design is presented. Recently, a promising scatter correction method for X-ray computed tomography (CT) that uses a checkerboard pattern of attenuating blockers (primary modulator) placed between the X-ray source and the object has been developed and experimentally verified. The blocker size, d, and the blocker transmission factor, α, are critical to the performance of the primary modulation method. In this work, an error caused by aliasing of primary whose magnitude depends on the choices of d and α, and the scanned object, is set as the object function to be minimized, with constraints including the X-ray focal spot, the physical size of the detector element, and the noise level. The optimization is carried out in two steps. In the first step, d is chosen as small as possible but should meet a lower-bound condition. In the second step, α should be selected to balance the error level in the scatter estimation and the noise level in the reconstructed image. The lower bound of d on our tabletop CT system is 0.83 mm. Numerical simulations suggest 0.6 < α < 0.8 is appropriate. Using a Catphan 600 phantom, a copper modulator (d = 0.89 mm, α = 0.70) expectedly outperforms an aluminum modulator (d = 2.83 mm, α = 0.90). With the aluminum modulator, our method reduces the average error of CT number in selected contrast rods from 371.4 to 25.4 Hounsfield units (HU) and enhances the contrast to noise ratio (CNR) from 10.9 to 17.2; when the copper modulator is used, the error is further reduced to 21.9 HU and the CNR is further increased to 19.2.

A unified framework for 3D radiation therapy and IMRT planning: plan optimization in the beamlet domain by constraining or regularizing the fluence map variations

The purpose of this work is to demonstrate that physical constraints on fluence gradients in 3D radiation therapy (RT) planning can be incorporated into beamlet optimization explicitly by direct constraint on the spatial variation of the fluence maps or implicitly by using total-variation regularization (TVR). The former method forces the fluence to vary in accordance with the known form of a wedged field and latter encourages the fluence to take the known form of the wedged field by requiring the derivatives of the fluence maps to be piece-wise constant. The performances of the proposed methods are evaluated by using a brain cancer case and a head and neck case. It is found that both approaches are capable of providing clinically sensible 3D RT solutions with monotonically varying fluence maps. For currently available 3D RT delivery schemes based on the use of customized physical or dynamic wedges, constrained optimization seems to be more useful because the optimized fields are directly deliverable. Working in the beamlet domain provides a natural way to model the spatial variation of the beam fluence. The proposed methods take advantage of the fact that 3D RT is a special form of intensity-modulated radiation therapy (IMRT) and finds the optimal plan by searching for fields with a certain type of spatial variation. The approach provides a unified framework for 3D CRT and IMRT plan optimization.

Image-domain shading correction for cone-beam CT without prior patient information

In the era of high‐precision radiotherapy, cone‐beam CT (CBCT) is frequently utilized for on‐board treatment guidance. However, CBCT images usually contain severe shading artifacts due to strong photon scatter from illumination of a large volume and non‐optimized patient‐specific data measurements, limiting the full clinical applications of CBCT. Many algorithms have been proposed to alleviate this problem by data correction on projections. Sophisticated methods have also been designed when prior patient information is available. Nevertheless, a standard, efficient, and effective approach with large applicability remains elusive for current clinical practice. In this work, we develop a novel algorithm for shading correction directly on CBCT images. Distinct from other image‐domain correction methods, our approach does not rely on prior patient information or prior assumption of patient data. In CBCT, projection errors (mostly from scatter and non‐ideal usage of bowtie filter) result in dominant low‐frequency shading artifacts in image domain. In circular scan geometry, these artifacts often show global or local radial patterns. Hence, the raw CBCT images are first preprocessed into the polar coordinate system. Median filtering and polynomial fitting are applied on the transformed image to estimate the low‐frequency shading artifacts (referred to as the bias field) angle‐by‐angle and slice‐by‐slice. The low‐pass filtering process is done firstly along the angular direction and then the radial direction to preserve image contrast. The estimated bias field is then converted back to the Cartesian coordinate system, followed by 3D low‐pass filtering to eliminate possible high‐frequency components. The shading‐corrected image is finally obtained as the uncorrected volume divided by the bias field. The proposed algorithm was evaluated on CBCT images of a pelvis patient and a head patient. Mean CT number values and spatial non‐uniformity on the reconstructed images were used as image quality metrics. Within selected regions of interest, the average CT number error was reduced from around 300 HU to 42 and 38 HU, and the spatial nonuniformity error was reduced from above 17.5% to 2.1% and 1.7% for the pelvis and the head patients, respectively. As our method suppresses only low‐frequency shading artifacts, patient anatomy and contrast were retained in the corrected images for both cases. Our shading correction algorithm on CBCT images offers several advantages. It has a high efficiency, since it is deterministic and directly operates on the reconstructed images. It requires no prior information or assumptions, which not only achieves the merits of CBCT‐based treatment monitoring by retaining the patient anatomy, but also facilitates its clinical use as an efficient image‐correction solution. PACS number(s): 87.57.C‐, 87.57.cp, 87.57.Q‐In the era of high-precision radiotherapy, cone-beam CT (CBCT) is frequently utilized for on-board treatment guidance. However, CBCT images usually contain severe shading artifacts due to strong photon scatter from illumination of a large volume and non-optimized patient-specific data measurements, limiting the full clinical applications of CBCT. Many algorithms have been proposed to alleviate this problem by data correction on projections. Sophisticated methods have also been designed when prior patient information is available. Nevertheless, a standard, efficient, and effective approach with large applicability remains elusive for current clinical practice. In this work, we develop a novel algorithm for shading correction directly on CBCT images. Distinct from other image-domain correction methods, our approach does not rely on prior patient information or prior assumption of patient data. In CBCT, projection errors (mostly from scatter and non-ideal usage of bowtie filter) result in dominant low-frequency shading artifacts in image domain. In circular scan geometry, these artifacts often show global or local radial patterns. Hence, the raw CBCT images are first preprocessed into the polar coordinate system. Median filtering and polynomial fitting are applied on the transformed image to estimate the low-frequency shading artifacts (referred to as the bias field) angle-by-angle and slice-by-slice. The low-pass filtering process is done firstly along the angular direction and then the radial direction to preserve image contrast. The estimated bias field is then converted back to the Cartesian coordinate system, followed by 3D low-pass filtering to eliminate possible high-frequency components. The shading-corrected image is finally obtained as the uncorrected volume divided by the bias field. The proposed algorithm was evaluated on CBCT images of a pelvis patient and a head patient. Mean CT number values and spatial non-uniformity on the reconstructed images were used as image quality metrics. Within selected regions of interest, the average CT number error was reduced from around 300 HU to 42 and 38 HU, and the spatial nonuniformity error was reduced from above 17.5% to 2.1% and 1.7% for the pelvis and the head patients, respectively. As our method suppresses only low-frequency shading artifacts, patient anatomy and contrast were retained in the corrected images for both cases. Our shading correction algorithm on CBCT images offers several advantages. It has a high efficiency, since it is deterministic and directly operates on the reconstructed images. It requires no prior information or assumptions, which not only achieves the merits of CBCT-based treatment monitoring by retaining the patient anatomy, but also facilitates its clinical use as an efficient image-correction solution. PACS number(s): 87.57.C-, 87.57.cp, 87.57.Q.

X-ray scatter correction for dedicated cone beam breast CT using a forward-projection model

Purpose The quality of dedicated cone‐beam breast CT (CBBCT) imaging is fundamentally limited by x‐ray scatter contamination due to the large irradiation volume. In this paper, we propose a scatter correction method for CBBCT using a novel forward‐projection model with high correction efficacy and reliability. Method We first coarsely segment the uncorrected, first‐pass, reconstructed CBBCT images into binary‐object maps and assign the segmented fibroglandular and adipose tissue with the correct attenuation coefficients based on the mean x‐ray energy. The modified CBBCT are treated as the prior images toward scatter correction. Primary signals are first estimated via forward projection on the modified CBBCT. To avoid errors caused by inaccurate segmentation, only sparse samples of estimated primary are selected for scatter estimation. A Fourier‐Transform based algorithm, herein referred to as local filtration hereafter, is developed to efficiently estimate the global scatter distribution on the detector. The scatter‐corrected images are obtained by removing the estimated scatter distribution from measured projection data. Results We evaluate the method performance on six patients with different breast sizes and shapes representing the general population. The results show that the proposed method effectively reduces the image spatial non‐uniformity from 8.27 to 1.91% for coronal views and from 6.50 to 3.00% for sagittal views. The contrast‐to‐deviation ratio is improved by an average factor of 1.41. Comparisons on the image details reveal that the proposed scatter correction successfully preserves fine structures of fibroglandular tissues that are lost in the segmentation process. Conclusion We propose a highly practical and efficient scatter correction algorithm for CBBCT via a forward‐projection model. The method is attractive in clinical CBBCT imaging as it is readily implementable on a clinical system without modifications in current imaging protocols or system hardware.