FDK Algorithm Research Articles

Compressed sensing with gradient total variation for low-dose CBCT reconstruction

This paper describes the improvement of convergence speed with gradient total variation (GTV) in compressed sensing (CS) for low-dose cone–beam computed tomography (CBCT) reconstruction. We derive a fast algorithm for the constrained total variation (TV)-based a minimum number of noisy projections. To achieve this task we combine the GTV with a TV-norm regularization term to promote an accelerated sparsity in the X-ray attenuation characteristics of the human body. The GTV is derived from a TV and enforces more efficient computationally and faster in convergence until a desired solution is achieved. The numerical algorithm is simple and derives relatively fast convergence. We apply a gradient projection algorithm that seeks a solution iteratively in the direction of the projected gradient while enforcing a non-negatively of the found solution. In comparison with the Feldkamp, Davis, and Kress (FDK) and conventional TV algorithms, the proposed GTV algorithm showed convergence in ≤18 iterations, whereas the original TV algorithm needs at least 34 iterations in reducing 50% of the projections compared with the FDK algorithm in order to reconstruct the chest phantom images. Future investigation includes improving imaging quality, particularly regarding X-ray cone–beam scatter, and motion artifacts of CBCT reconstruction.

A low-complexity 2-point step size gradient projection method with selective function evaluations for smoothed total variation based CBCT reconstructions

The Barzilai–Borwein (BB) 2-point step size gradient method is receiving attention for accelerating Total Variation (TV) based CBCT reconstructions. In order to become truly viable for clinical applications, however, its convergence property needs to be properly addressed. We propose a novel fast converging gradient projection BB method that requires ‘at most one function evaluation’ in each iterative step. This Selective Function Evaluation method, referred to as GPBB-SFE in this paper, exhibits the desired convergence property when it is combined with a ‘smoothed TV’ or any other differentiable prior. This way, the proposed GPBB-SFE algorithm offers fast and guaranteed convergence to the desired 3DCBCT image with minimal computational complexity. We first applied this algorithm to a Shepp–Logan numerical phantom. We then applied to a CatPhan 600 physical phantom (The Phantom Laboratory, Salem, NY) and a clinically-treated head-and-neck patient, both acquired from the TrueBeam™ system (Varian Medical Systems, Palo Alto, CA). Furthermore, we accelerated the reconstruction by implementing the algorithm on NVIDIA GTX 480 GPU card. We first compared GPBB-SFE with three recently proposed BB-based CBCT reconstruction methods available in the literature using Shepp–Logan numerical phantom with 40 projections. It is found that GPBB-SFE shows either faster convergence speed/time or superior convergence property compared to existing BB-based algorithms. With the CatPhan 600 physical phantom, the GPBB-SFE algorithm requires only 3 function evaluations in 30 iterations and reconstructs the standard, 364-projection FDK reconstruction quality image using only 60 projections. We then applied the algorithm to a clinically-treated head-and-neck patient. It was observed that the GPBB-SFE algorithm requires only 18 function evaluations in 30 iterations. Compared with the FDK algorithm with 364 projections, the GPBB-SFE algorithm produces visibly equivalent quality CBCT image for the head-and-neck patient with only 180 projections, in 131.7 s, further supporting its clinical applicability.

A hybrid reconstruction algorithm for fast and accurate 4D cone-beam CT imaging.

4D cone beam CT (4D-CBCT) has been utilized in radiation therapy to provide 4D image guidance in lung and upper abdomen area. However, clinical application of 4D-CBCT is currently limited due to the long scan time and low image quality. The purpose of this paper is to develop a new 4D-CBCT reconstruction method that restores volumetric images based on the 1-min scan data acquired with a standard 3D-CBCT protocol. The model optimizes a deformation vector field that deforms a patient-specific planning CT (p-CT), so that the calculated 4D-CBCT projections match measurements. A forward-backward splitting (FBS) method is invented to solve the optimization problem. It splits the original problem into two well-studied subproblems, i.e., image reconstruction and deformable image registration. By iteratively solving the two subproblems, FBS gradually yields correct deformation information, while maintaining high image quality. The whole workflow is implemented on a graphic-processing-unit to improve efficiency. Comprehensive evaluations have been conducted on a moving phantom and three real patient cases regarding the accuracy and quality of the reconstructed images, as well as the algorithm robustness and efficiency. The proposed algorithm reconstructs 4D-CBCT images from highly under-sampled projection data acquired with 1-min scans. Regarding the anatomical structure location accuracy, 0.204 mm average differences and 0.484 mm maximum difference are found for the phantom case, and the maximum differences of 0.3-0.5 mm for patients 1-3 are observed. As for the image quality, intensity errors below 5 and 20 HU compared to the planning CT are achieved for the phantom and the patient cases, respectively. Signal-noise-ratio values are improved by 12.74 and 5.12 times compared to results from FDK algorithm using the 1-min data and 4-min data, respectively. The computation time of the algorithm on a NVIDIA GTX590 card is 1-1.5 min per phase. High-quality 4D-CBCT imaging based on the clinically standard 1-min 3D CBCT scanning protocol is feasible via the proposed hybrid reconstruction algorithm.

SU‐E‐I‐93: Improved Imaging Quality for Multislice Helical CT Via Sparsity Regularized Iterative Image Reconstruction Method Based On Tensor Framelet

Purpose:Inspired by compressive sensing, sparsity regularized iterative reconstruction method has been extensively studied. However, its utility pertinent to multislice helical 4D CT for radiotherapy with respect to imaging quality, dose, and time has not been thoroughly addressed. As the beginning of such an investigation, this work carries out the initial comparison of reconstructed imaging quality between sparsity regularized iterative method and analytic method through static phantom studies using a state‐of‐art 128‐channel multi‐slice Siemens helical CT scanner.Methods:In our iterative method, tensor framelet (TF) is chosen as the regularization method for its superior performance from total variation regularization in terms of reduced piecewise‐constant artifacts and improved imaging quality that has been demonstrated in our prior work. On the other hand, X‐ray transforms and its adjoints are computed on‐the‐fly through GPU implementation using our previous developed fast parallel algorithms with O(1) complexity per computing thread. For comparison, both FDK (approximate analytic method) and Katsevich algorithm (exact analytic method) are used for multislice helical CT image reconstruction.Results:The phantom experimental data with different imaging doses were acquired using a state‐of‐art 128‐channel multi‐slice Siemens helical CT scanner. The reconstructed image quality was compared between TF‐based iterative method, FDK and Katsevich algorithm with the quantitative analysis for characterizing signal‐to‐noise ratio, image contrast, and spatial resolution of high‐contrast and low‐contrast objects.Conclusion:The experimental results suggest that our tensor framelet regularized iterative reconstruction algorithm improves the helical CT imaging quality from FDK and Katsevich algorithm for static experimental phantom studies that have been performed.

SU‐D‐12A‐01: An Inter‐Projection Interpolation (IPI) Approach for the Synchronized Moving Grid (SMOG) to Reduce Dose in Cone Beam CT

Purpose:Synchronized moving grid is a promising technique to reduce scatter and ghost artifacts in cone beam computed tomography (CBCT). However, it requires 2 projections in the same gantry angle to obtain full information due to signal blockage by the grid. We proposed an inter‐projection interpolation (IPI) method to estimate blocked signals, which may reduce the scan time and the dose. This study aims to provide a framework to achieve a balance between speed, dose and image quality.Methods:The IPI method is based on the hypothesis that an abrupt signal in a projection can be well predicted by the information in the two immediate neighboring projections if the gantry angle step is small. The study was performed on a Catphan and a head phantom. The SMOG was simulated by erasing the information (filling with “0”) of the areas in each projection corresponding to the grid. An IPI algorithm was applied on each projection to recover the erased information. FDK algorithm was used to reconstruct CBCT images for the IPI‐processed projections, and compared with the original image in term of signal to noise ratio (SNR) measured in the whole reconstruction image range. The effect of gantry angle step was investigated by comparing the CBCT images from projection sets of various gantry intervals, with IPI‐predicted projections to fill the missing projection in the interval.Results:The IPI procession time was 1.79s±0.53s for each projection. SNR after IPI was 29.0db and 28.1db for the Catphan and head phantom, respectively, comparing to 15.3db and 22.7db for an inpainting based interpolation technique. SNR was 28.3, 28.3, 21.8, 19.3 and 17.3 db for gantry angle intervals of 1, 1.5, 2, 2.5 and 3 degrees, respectively.Conclusion:IPI is feasible to estimate the missing information, and achieve an reasonable CBCT image quality with reduced dose and scan time.This study is supported by NIH/NCI grant 1R01CA166948‐01

A multi-source inverse-geometry CT system: initial results with an 8 spot x-ray source array

We present initial experimental results of a rotating-gantry multi-source inverse-geometry CT (MS-IGCT) system. The MS-IGCT system was built with a single module of 2 × 4 x-ray sources and a 2D detector array. It produced a 75 mm in-plane field-of-view (FOV) with 160 mm axial coverage in a single gantry rotation. To evaluate system performance, a 2.5 inch diameter uniform PMMA cylinder phantom, a 200 µm diameter tungsten wire, and a euthanized rat were scanned. Each scan acquired 125 views per source and the gantry rotation time was 1 s per revolution. Geometric calibration was performed using a bead phantom. The scanning parameters were 80 kVp, 125 mA, and 5.4 µs pulse per source location per view. A data normalization technique was applied to the acquired projection data, and beam hardening and spectral nonlinearities of each detector channel were corrected. For image reconstruction, the projection data of each source row were rebinned into a full cone beam data set, and the FDK algorithm was used. The reconstructed volumes from upper and lower source rows shared an overlap volume which was combined in image space. The images of the uniform PMMA cylinder phantom showed good uniformity and no apparent artifacts. The measured in-plane MTF showed 13 lp cm−1 at 10% cutoff, in good agreement with expectations. The rat data were also reconstructed reliably. The initial experimental results from this rotating-gantry MS-IGCT system demonstrated its ability to image a complex anatomical object without any significant image artifacts and to achieve high image resolution and large axial coverage in a single gantry rotation.

Comparison of Parallel Computing Methods for Fast Cone-Beam Reconstruction with Similar Optimization Strategies

To investigate the performance of acceleration technologies for FDK algorithm, two of the most common high-performance computing hardware, multi-core CPU and GPU, are involved in our experiment. Both runtime and accuracy are regarded as the standards to evaluate the performance of four different programming methods: OpenMP, GLSL, CUDA and OpenCL. All the methods are estimated with comparable optimization strategies. The experimental results show that GPU has higher efficiency than multi-core CPU for fast cone-beam reconstruction, meanwhile CUDA is the best choice for programming on the multi-processor featured GPU.

Application of three-dimensional medical image registration algorithm in image-guided radiotherapy

To acquire an accurate patient positioning in image-guided radiotherapy, an improved Demons deformable registration method was developed. The FDK algorithm was adopted to reconstruct Cone Beam CT( CBCT) and the reconstruction result was visualized by a volume rendering method with Visualization ToolKit( VTK). Based on the Insight segmentation and registration ToolKit( ITK), the Demons algorithm was completed incorporating the gradient information of fixed image and floating image by the concept of symmetric gradient, and a new formula of Demons force was demonstrated.Registrion experiments were carried out using medical images both from single modality and multi-modality. The results show that the improved Demons algorithm achieves a faster convergence speed and a higher precision compared with the original demons algorithm, which indicates that the Demons algorithm based on symmetric gradient is more suitable for the registration of CBCT reconstruction image and CT plan image in image-guided radiotherapy.

SU-E-I-14: Improvement of Four Dimensional Cone Beam CT Image Quality with Iterative Reconstruction

Purpose: Four‐dimensional cone beam CT (4D‐CBCT) is well known as powerful modality for image guided radiation therapy. Conventionally, it is reconstructed by sorting the X‐ray projection images into each respiratory phase according to a breathing signal using the FDK algorithm. This usually leads to inadequate number of projections in each phase, resulting in low quality 4D‐CBCT images with obvious streaking artifacts. We tried to improve the image quality for 4D CBCT using iterative reconstruction method (ML‐convex) and compared with the images by FDK in SNR of the reconstructed images. Methods: We used ML‐convex algorithm, which has the ability to reconstruct CBCT images from a few number of noisy x‐ray projections by taking knowledge of x‐ray photon statistics into account. We compared the image quality of 4D CBCT by ML‐convex with that by FDK using projection images acquired with different rotational speeds by XVI 5.0 (Elekta). Projection images were sorted by 10 phases for both reconstruction algorithms. A phantom study and patient study were performed. The convergence rate and reconstruction accuracy were evaluated using Catphan‐600 physical phantom. Results: Image quality of 4D‐CBCT is substantially enhanced by the ML‐convex algorithm. Streaking artifacts, commonly presented in the image reconstructed by FDK algorithm, are almost suppressed in spite of the small number of projections. Quantitative evaluations indicated that, compared with the FDK results, ML‐convex method improves signal‐to‐noise‐ratio (SNR) and reconstructed more accurate CT value. Conclusion: The ML‐convex algorithm yielded images with higher SNR and more accurate CT value than those produced by FDK algorithm. This Result will enable us to apply 4D CBCT by ML‐convex algorithm to Image Guided Adaptive Radiation Therapy and patient daily CBCT‐based treatment localization in real clinical environments with the higher computational efficiency.

TU‐G‐141‐05: Limited Field‐Of‐View Cone‐Beam CT Reconstruction for Adaptive Radiotherapy

Purpose: Reconstructing CBCT only inside a relatively small circular field of view (FOV) is preferred for adaptive radiotherapy due to the reduced imaging dose, possible short computation time, and sufficient anatomy information for treatment adaptation. Current analytical or iterative reconstruction approaches encounter a truncation problem with degraded image quality inside the FOV. Anatomy outside the FOV is also missing, which is required for dose calculation. The purpose of this study is to develop a technique to obtain CBCT images with high quality inside the FOV and lower quality outside the FOV. Methods: CBCT data acquisition is conducted first at all x‐ray projection angles with a standard FOV to cover the whole body but at a very low mAs. A reconstruction is conducted via FDK algorithm, yielding a noisy CBCT image. X‐ray projection is also acquired with a standard mAs for a small FOV of interest at sparse projection angles. We then forward project the noisy CBCT image outside the small FOV to those sparsely acquired projection angles and subtract the results from the high‐mAs projection data. A high‐quality CBCT image inside the FOV is reconstructed using the updated projection data at those sparse angles via our fast GPU‐based tight‐frame iterative CBCT reconstruction algorithm. Finally, the noisy image outside the FOV and the high‐quality image inside the FOV are merged. Our algorithm is validated in digital NCAT phantom cases. Results: It was found that the proposed method can remove the noise and truncation artifacts effectively and preserve anatomical features inside the FOV. It attains a relative root mean square (RRMS) error of 5.94%. Because of GPU implementation, the computational efficiency is high for clinical applications. Conclusion: The developed CBCT reconstruction method can provide CBCT images with high‐quality FOV for adaptive radiotherapy.

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.

GPU-based parallel implementation of FDK algorithm for cone-beam CT

To improve the reconstruction speed of the FDK algorithm,this paper presented a fast algorithm based on the graphics processing unit(GPU).The method acquired higher computational efficiency through more careful optimization techniques,including reasonable mode of thread assigning,collecting and pre-computing the variables which were irrelevant with the voxel and the decreasing of number of global memory accesses.The simulation results show that while the fully optimized algorithm makes no precision reduction,the reconstruction time for 2563 is only 0.5 seconds and for 5123 is only 2.5 seconds,which is a big advance in comparison with the latest research findings.

Fast Low-Dose Reconstruction From Truncated Data in Dental CT

To reduce the radiation dose in dental computed tomography (CT), backprojection-filtration (BPF) algorithm is the preferred choice as it can reconstruct images from truncated data within limited scanning angle, thereby reducing radiation dose and avoiding irradiation to the brain. However, the integral interval of backprojection is variable for every PI-line which causes the calculation efficiency and parallel performance to be low. In this paper, the tent BPF method (T-BPF) was developed, which was performed by firstly rearranging the cone-beam data to tent-like parallel-beam data, and then applying the proposed BPF-type algorithm to reconstruct images from the rearranged data. T-BPF turns the variable integral interval of backprojection into fixed integral interval, which means the reconstruction efficiency and the parallel performance of T-BPF are improvements over those of the original BPF algorithm. The experiments of numerical simulation and real data reconstruction show that the reconstruction efficiency of T-BPF is faster than the original BPF algorithm and the FDK algorithm in the case of comparable reconstruction quality. The results demonstrate that the proposed T-BPF is good at achieving fast low-dose reconstruction from truncated projection data in dental CT.

Four‐dimensional cone beam CT reconstruction and enhancement using a temporal nonlocal means method

Four-dimensional cone beam computed tomography (4D-CBCT) has been developed to provide respiratory phase-resolved volumetric imaging in image guided radiation therapy. Conventionally, it is reconstructed by first sorting the x-ray projections into multiple respiratory phase bins according to a breathing signal extracted either from the projection images or some external surrogates, and then reconstructing a 3D CBCT image in each phase bin independently using FDK algorithm. This method requires adequate number of projections for each phase, which can be achieved using a low gantry rotation or multiple gantry rotations. Inadequate number of projections in each phase bin results in low quality 4D-CBCT images with obvious streaking artifacts. 4D-CBCT images at different breathing phases share a lot of redundant information, because they represent the same anatomy captured at slightly different temporal points. Taking this redundancy along the temporal dimension into account can in principle facilitate the reconstruction in the situation of inadequate number of projection images. In this work, the authors propose two novel 4D-CBCT algorithms: an iterative reconstruction algorithm and an enhancement algorithm, utilizing a temporal nonlocal means (TNLM) method. The authors define a TNLM energy term for a given set of 4D-CBCT images. Minimization of this term favors those 4D-CBCT images such that any anatomical features at one spatial point at one phase can be found in a nearby spatial point at neighboring phases. 4D-CBCT reconstruction is achieved by minimizing a total energy containing a data fidelity term and the TNLM energy term. As for the image enhancement, 4D-CBCT images generated by the FDK algorithm are enhanced by minimizing the TNLM function while keeping the enhanced images close to the FDK results. A forward-backward splitting algorithm and a Gauss-Jacobi iteration method are employed to solve the problems. The algorithms implementation on GPU is designed to avoid redundant and uncoalesced memory access, in order to ensure a high computational efficiency. Our algorithms have been tested on a digital NURBS-based cardiac-torso phantom and a clinical patient case. The reconstruction algorithm and the enhancement algorithm generate visually similar 4D-CBCT images, both better than the FDK results. Quantitative evaluations indicate that, compared with the FDK results, our reconstruction method improves contrast-to-noise-ratio (CNR) by a factor of 2.56-3.13 and our enhancement method increases the CNR by 2.75-3.33 times. The enhancement method also removes over 80% of the streak artifacts from the FDK results. The total computation time is 509-683 s for the reconstruction algorithm and 524-540 s for the enhancement algorithm on an NVIDIA Tesla C1060 GPU card. By innovatively taking the temporal redundancy among 4D-CBCT images into consideration, the proposed algorithms can produce high quality 4D-CBCT images with much less streak artifacts than the FDK results, in the situation of inadequate number of projections.

Noise suppression in reconstruction of low‐Z target megavoltage cone‐beam CT images

To improve the image contrast-to-noise (CNR) ratio for low-Z target megavoltage cone-beam CT (MV CBCT) using a statistical projection noise suppression algorithm based on the penalized weighted least-squares (PWLS) criterion. Projection images of a contrast phantom, a CatPhan(®) 600 phantom and a head phantom were acquired by a Varian 2100EX LINAC with a low-Z (Al) target and low energy x-ray beam (2.5 MeV) at a low-dose level and at a high-dose level. The projections were then processed by minimizing the PWLS objective function. The weighted least square (WLS) term models the noise of measured projection and the penalty term enforces the smoothing constraints of the projection image. The variance of projection data was chosen as the weight for the PWLS objective function and it determined the contribution of each measurement. An anisotropic quadratic form penalty that incorporates the gradient information of projection image was used to preserve edges during noise reduction. Low-Z target MV CBCT images were reconstructed by the FDK algorithm after each projection was processed by the PWLS smoothing. Noise in low-Z target MV CBCT images were greatly suppressed after the PWLS projection smoothing, without noticeable sacrifice of the spatial resolution. Depending on the choice of smoothing parameter, the CNR of selected regions of interest in the PWLS processed low-dose low-Z target MV CBCT image can be higher than the corresponding high-dose image. The CNR of low-Z target MV CBCT images was substantially improved by using PWLS projection smoothing. The PWLS projection smoothing algorithm allows the reconstruction of high contrast low-Z target MV CBCT image with a total dose of as low as 2.3 cGy.

A cone beam computed tomography inspection method for fuel rod cladding tubes

Fuel rods in nuclear power plants consist of UO2 pellets enclosed in Zirconium alloy (Zircaloy) cladding tube, which is composed of a body and a plug. The body is manufactured separately from the plug and, before its use, the plug is welded with the body. It is vitally important for the welding zone to remain free from defects after the fuel pellets are loaded into the cladding tube to prevent the radioactive fission products from leaking. X-ray computed tomography (CT) is in principle a feasible inspection method for the welding zone, but it faces several challenges due to the high attenuation of Zircaloy. In this paper, a cone beam CT method is proposed to address these issues and perform the welding flaw inspection. A Zircaloy compensator is adopted to narrow the signal range, a structure-based background removal technique to reveal the defects, a linear extension technique to determine the reference X-ray intensity signal and FDK algorithm to reconstruct the slice images. A prototype system, based on X-ray tube source and flat panel detector, has been developed and the experiments in this system have demonstrated that the welding void and the incomplete joint penetrations could be detected by this method. This approach may find applications in the quality control of nuclear fuel rods.

WE‐G‐217BCD‐06: Fully Incorporated Scanning Geometry for Improved Accuracy in C‐Arm CBCT Image Reconstruction

The adoption of C-arm cone-beam CT (CBCT) can minimize interruption to the interventional workflow. However, C-arm gantry rotation can be susceptible to gravity and mechanical instability, therefore resulting images with contamination of tilting and wobbling motion. The purpose of this work is to investigate and demonstrate potential improvement of C-arm CBCT images by tailoring and applying an innovative iterative algorithm that can fully incorporate accurate scanning geometry. A clinical C-arm CBCT system (Toshiba Infinix-i, Japan) was used for collecting projection data of a patient's brain with aneurysm. A mask scan was performed before contrast was injected, and a contrast scan was performed during continuous contrast feeding. During each scan, 108 projections were acquired over a range of approximately 200 degrees within about 4.6 seconds. Logarithm subtraction was then carried out view by view to obtain 108 projections of virtually only the vasculature. An iterative algorithm, referred to as the ASD-POCS algorithm, was modified to fully incorporate calibration data characterizing the actual scan geometry that deviates from a circular trajectory due to gantry tilting and wobbling. We then applied both FDK and ASD-POCS algorithms to reconstructing image from the acquired patient data. In FDK reconstructions without considering C-arm tilting and wobbling motion, artifacts can be observed, which break vessel continuity and compromise image's clinical utility. We then performed FDK reconstructions by incorporating the system geometry in the back-projection step and obtained improved vessel continuity. Finally we applied the ASD- POCS algorithm by incorporating calibration data in the forward- and back- projector, and obtained reconstructions with further improvement on the recovery of small, secondary vascular branches. Appropriately developed iterative algorithms can improve C-arm CBCT image quality by fully incorporating scanning geometry, and can potentially enable spatial-resolution demanding applications which can be challenging to achieve with the FDK algorithm.

WE-G-217BCD-07: Implementation and Evaluation of Helical On-Board CBCT and Exact Image Reconstruction.

Longitudinal coverage of CBCT, which is 17 cm for head scan and 15.5 cm for body scan, is not enough to cover the entire PTV for over 90% of head/neck and gastrointestinal/genitourinary/gynecologic patients if lymph nodes are involved. Helical CBCT, which was accomplished using external beam LINAC in its research mode, is one promising way to extend the CBCT longitudinal coverage. Aim of this study is to compare Katsevich's exact algorithm with traditional FDK algorithm for helical CBCT image reconstruction. CBCT projection raw data were acquired on a TrueBeam LINAC machine (Varian Medical Systems) in the research mode in helical trajectories that encompass a 360 degree rotation, 25 cm pitch, 100 kVp, 80 mA, and 25 ms, with a Catphan 600. Reconstruction was done with Katsevich's exact and FDK approximate algorithms. Scatter correction, beam-hardening correction, and non-uniform gantry angle correction, are performed on projection data to reduce artifacts and noise. Image qualities (CT number accuracy, uniformity, SNR) were evaluated and compared between the reconstruction algorithms. Images reconstructed by Katsevich's algorithm show better qualities, compared to ones by FDK algorithm and HU numbers have higher uniformity and accuracy. The HU-density calibration curve closely conforms to the manufacturer recommended values. The level of noise computed as the standard deviation in the phantom uniform region is 28.07 for the Katsevich algorithm, compared to 44.64 for the FDK algorithm. Katsevich's exact reconstruction algorithm provided better image qualities than FDK for helical CBCT scans. This result will very useful for our ongoing investigation of helical CBCT, which would lead to improvement of CBCT longitudinal coverage of PTV and would be essential for future image-guided adaptive radiation therapy applications. Varian Research Agreement with Washington University in St. Louis.

TU-A-213CD-07: Compressed Sensing Based Four Dimensional Cone-Beam Computed Tomography Reconstruction by Continuation Accelerated Nesterov's Descent

Purpose: Compressed sensing based cone‐beam reconstruction is introduced to reduce streaking artifacts due to under‐sampling in four dimensional (4D) cone‐beam computed tomography(CBCT). This reconstruction, however, is typically time‐consuming, especially for 4D CBCT. We propose a novel approach, which introduces a first‐order methods, called continuation accelerated Nesterov's descent, to improve convergence rate. Methods: We extract the respiratory signal directly from projections, sort them into ten subsets, and reconstruct each subset into a 3D CBCT by compressed sensing based total‐variation minimization. The reconstruction iteration is solved by Nesterov's descent algorithm. In each loop, we adapt the step size by sufficient reducing global Lipschitz constant, and update variants by gradient‐mapping parameters to proximal points. The proposed method is assessed by a thorax phantom and a patient, which are scanned with a CBCTscanner. The reconstructed data is compared among FDK algorithm, projection onto convex sets (POCS) which is a steepest decent based optimization, and our method. Results: A region of homogeneous voxel values is manually selected, and the root‐mean‐square‐ error between CBCT and CT in this region is defined as streaking artifacts. It's reduced 27.2% in phantom data, when our method is compared to traditional FDK methods for 2 minute scan. Correlation ratio between CBCT and CT is increased for 10.2% when our method is compared to FDK for patient data. For the convergence rate, our method only needs 25 iterations to get the same total‐variation residual of POCS at 250 iterations. Also for other cut‐offs, it seems an order of magnitude faster. Conclusions: Our proposed method decreases the streaking artifacts and convergence time in 4D CBCT reconstruction. The image quality assessment suggests that our method has improved image quality and better correlation.

TU-A-213CD-08: A Novel 2-Point Step Size Gradient Method for Regularized Total Variation Based CBCT Reconstructions

Purpose: To develop a novel, fast converging 2-point step size gradient method for CBCT reconstructions and show its clinical feasibility. Methods: The Barzilai-Borwein (BB) 2-point step size gradient method is getting recent attentions for accelerating Total Variation (TV) based CBCT reconstructions. In order to become truly viable for clinical applications, however, the iterative framework needs to ensure guaranteed convergence by carefully defining the cost function and the reconstruction algorithm. We propose a novel approach that combines an unconstrained BB (UBB) method and the gradient projection (GP) method enforcing non-negativity constraints. This way, the proposed GP-UBB algorithm inherits both the fast converging property of the UBB and the robust convergence property of GP. We applied this algorithm to both Shepp-Logan numerical phantom and a clinically-treated head-and-neck patient acquired from the TrueBeam system (Varian Medical Systems, Palo Alto, CA). Furthermore, we accelerated the reconstruction by implementing the algorithm on NVIDIA GTX 295 GPU card. Results: We first compared GPUBB with a recently proposed BB- based CBCT reconstruction method available in the literature and the well- known ASD-POCS algorithm using Shepp-Logan numerical phantom with 40 projections. As the iterations progress, GPUBB is found to converge much faster than the other two algorithms. Therefore, GPUBB commands superior image quality with less number of iterations. We then applied the algorithm to a clinically-treated head-and-neck patient. It was observed that, compared with the FDK algorithm with 364 projections, our GPUBB algorithm produces a visually equivalent quality CBCT image with only 120 projections, further supporting its practical value for realizing low-dose iterative CBCT reconstructions. Conclusions: By developing a novel, fast converging 2-step size gradient method for a CBCT reconstruction problem, we enhanced the clinical applicability of the compressive sensing based iterative reconstruction by guaranteeing convergence (i.e., consistent reconstructions) and accelerating the reconstruction speed (i.e., less number of iterations).