arXiv subjects

Steve B. Jiang

Publications and source records attributed to Steve B. Jiang.

At least 19 recordsLinked to original sources

arXiv2024

Fast Monte Carlo Dose Calculation in Proton Therapy

This article examines the critical role of fast Monte Carlo dose calculations in advancing proton therapy techniques, particularly in the context of increasing treatment customization and precision. As adaptive radiotherapy and other patient-specific approaches evolve, the need for accurate and precise dose calculations, essential for techniques like proton-based stereotactic radiosurgery, becomes more prominent. These calculations, however, are time-intensive, with the treatment planning/optimization process constrained by the achievable speed of dose computations. Thus, enhancing the speed of Monte Carlo methods is vital, as it not only facilitates the implementation of novel treatment modalities but also improves the optimality of treatment plans. Today, the state-of-the-art in Monte Carlo dose calculation speeds is 106 - 107 protons per second. This review highlights the latest advancements in fast Monte Carlo dose calculations that have led to such speeds, including emerging artificial intelligence-based techniques, and discusses their application in both current and emerging proton therapy strategies.

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arXiv2018

Intelligent Inverse Treatment Planning via Deep Reinforcement Learning, a Proof-of-Principle Study in High Dose-rate Brachytherapy for Cervical Cancer

Inverse treatment planning in radiation therapy is formulated as optimization problems. The objective function and constraints consist of multiple terms designed for different clinical and practical considerations. Weighting factors of these terms are needed to define the optimization problem. While a treatment planning system can solve the optimization problem with given weights, adjusting the weights for high plan quality is performed by human. The weight tuning task is labor intensive, time consuming, and it critically affects the final plan quality. An automatic weight-tuning approach is strongly desired. The weight tuning procedure is essentially a decision making problem. Motivated by the tremendous success in deep learning for decision making with human-level intelligence, we propose a novel framework to tune the weights in a human-like manner. Using treatment planning in high-dose-rate brachytherapy as an example, we develop a weight tuning policy network (WTPN) that observes dose volume histograms of a plan and outputs an action to adjust organ weights, similar to the behaviors of a human planner. We train the WTPN via end-to-end deep reinforcement learning. Experience replay is performed with the epsilon greedy algorithm. Then we apply the trained WTPN to guide treatment planning of testing patient cases. The trained WTPN successfully learns the treatment planning goals to guide the weight tuning process. On average, the quality score of plans generated under the WTPN's guidance is improved by ~8.5% compared to the initial plan with arbitrary weights, and by 10.7% compared to the plans generated by human planners. To our knowledge, this is the first tool to adjust weights for the treatment planning in a human-like fashion based on learnt intelligence. The study demonstrates potential feasibility to develop intelligent treatment planning system via deep reinforcement learning.

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arXiv2017

Intelligent Parameter Tuning in Optimization-based Iterative CT Reconstruction via Deep Reinforcement Learning

A number of image-processing problems can be formulated as optimization problems. The objective function typically contains several terms specifically designed for different purposes. Parameters in front of these terms are used to control the relative weights among them. It is of critical importance to tune these parameters, as quality of the solution depends on their values. Tuning parameter is a relatively straightforward task for a human, as one can intelligently determine the direction of parameter adjustment based on the solution quality. Yet manual parameter tuning is not only tedious in many cases, but becomes impractical when a number of parameters exist in a problem. Aiming at solving this problem, this paper proposes an approach that employs deep reinforcement learning to train a system that can automatically adjust parameters in a human-like manner. We demonstrate our idea in an example problem of optimization-based iterative CT reconstruction with a pixel-wise total-variation regularization term. We set up a parameter tuning policy network (PTPN), which maps an CT image patch to an output that specifies the direction and amplitude by which the parameter at the patch center is adjusted. We train the PTPN via an end-to-end reinforcement learning procedure. We demonstrate that under the guidance of the trained PTPN for parameter tuning at each pixel, reconstructed CT images attain quality similar or better than in those reconstructed with manually tuned parameters.

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arXiv2015

An Analytic Linear Accelerator Source Model for Monte Carlo Dose Calculations. I. Model Representation and Construction

Monte Carlo (MC) simulation is considered as the most accurate method for radiation dose calculations. Accuracy of a source model for a linear accelerator is critical for the overall dose calculation accuracy. In this paper, we presented an analytical source model that we recently developed for GPU-based MC dose calculations. A key concept called phase-space-ring (PSR) was proposed. It contained a group of particles that are of the same type and close in energy and radial distance to the center of the phase-space plane. The model parameterized probability densities of particle location, direction and energy for each primary photon PSR, scattered photon PSR and electron PSR. For a primary photon PSRs, the particle direction is assumed to be from the beam spot. A finite spot size is modeled with a 2D Gaussian distribution. For a scattered photon PSR, multiple Gaussian components were used to model the particle direction. The direction distribution of an electron PSRs was also modeled as a 2D Gaussian distribution with a large standard deviation. We also developed a method to analyze a phase-space file and derive corresponding model parameters. To test the accuracy of our linac source model, dose distributions of different open fields in a water phantom were calculated using our source model and compared to those directly calculated using the reference phase-space file. The average distance-to-agreement (DTA) was within 1 mm for the depth dose in the build-up region and beam penumbra regions. The root-mean-square (RMS) dose difference was within 1.1% for dose profiles at inner and outer beam regions. The maximal relative difference of output factors was within 0.5%. Good agreements were also found in an IMRT prostate patient case and an IMRT head-and-neck case. These results demonstrated the efficacy of our source model in terms of accurately representing a reference phase-space file.

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arXiv2015

An Analytic Linear Accelerator Source Model for Monte Carlo dose calculations. II. Model Utilization in a GPU-based Monte Carlo Package and Automatic Source Commissioning

We recently built an analytical source model for GPU-based MC dose engine. In this paper, we present a sampling strategy to efficiently utilize this source model in GPU-based dose calculation. Our source model was based on a concept of phase-space-ring (PSR). This ring structure makes it effective to account for beam rotational symmetry, but not suitable for dose calculations due to rectangular jaw settings. Hence, we first convert PSR source model to its phase-space let (PSL) representation. Then in dose calculation, different types of sub-sources were separately sampled. Source sampling and particle transport were iterated. So that the particles being sampled and transported simultaneously are of same type and close in energy to alleviate GPU thread divergence. We also present an automatic commissioning approach to adjust the model for a good representation of a clinical linear accelerator . Weighting factors were introduced to adjust relative weights of PSRs, determined by solving a quadratic minimization problem with a non-negativity constraint. We tested the efficiency gain of our model over a previous source model using PSL files. The efficiency was improved by 1.70 ~ 4.41, due to the avoidance of long data reading and transferring. The commissioning problem can be solved in ~20 sec. Its efficacy was tested by comparing the doses computed using the commissioned model and the uncommissioned one, with measurements in different open fields in a water phantom under a clinical Varian Truebeam 6MV beam. For the depth dose curves, the average distance-to-agreement was improved from 0.04~0.28 cm to 0.04~0.12 cm for build-up region and the root-mean-square (RMS) dose difference after build-up region was reduced from 0.32%~0.67% to 0.21%~0.48%. For lateral dose profiles, RMS difference was reduced from 0.31%~2.0% to 0.06%~0.78% at inner beam and from 0.20%~1.25% to 0.10%~0.51% at outer beam.

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arXiv2015

Multi-GPU implementation of a VMAT treatment plan optimization algorithm

VMAT optimization is a computationally challenging problem due to its large data size, high degrees of freedom, and many hardware constraints. High-performance graphics processing units have been used to speed up the computations. However, its small memory size cannot handle cases with a large dose-deposition coefficient (DDC) matrix. This paper is to report an implementation of our column-generation based VMAT algorithm on a multi-GPU platform to solve the memory limitation problem. The column-generation approach generates apertures sequentially by solving a pricing problem (PP) and a master problem (MP) iteratively. The DDC matrix is split into four sub-matrices according to beam angles, stored on four GPUs in compressed sparse row format. Computation of beamlet price is accomplished using multi-GPU. While the remaining steps of PP and MP problems are implemented on a single GPU due to their modest computational loads. A H&N patient case was used to validate our method. We compare our multi-GPU implementation with three single GPU implementation strategies: truncating DDC matrix (S1), repeatedly transferring DDC matrix between CPU and GPU (S2), and porting computations involving DDC matrix to CPU (S3). Two more H&N patient cases and three prostate cases were also used to demonstrate the advantages of our method. Our multi-GPU implementation can finish the optimization within ~1 minute for the H&N patient case. S1 leads to an inferior plan quality although its total time was 10 seconds shorter than the multi-GPU implementation. S2 and S3 yield same plan quality as the multi-GPU implementation but take ~4 minutes and ~6 minutes, respectively. High computational efficiency was consistently achieved for the other 5 cases. The results demonstrate that the multi-GPU implementation can handle the large-scale VMAT optimization problem efficiently without sacrificing plan quality.

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arXiv2015

An OpenCL-based Monte Carlo dose calculation engine (oclMC) for coupled photon-electron transport

Monte Carlo (MC) method has been recognized the most accurate dose calculation method for radiotherapy. However, its extremely long computation time impedes clinical applications. Recently, a lot of efforts have been made to realize fast MC dose calculation on GPUs. Nonetheless, most of the GPU-based MC dose engines were developed in NVidia CUDA environment. This limits the code portability to other platforms, hindering the introduction of GPU-based MC simulations to clinical practice. The objective of this paper is to develop a fast cross-platform MC dose engine oclMC using OpenCL environment for external beam photon and electron radiotherapy in MeV energy range. Coupled photon-electron MC simulation was implemented with analogue simulations for photon transports and a Class II condensed history scheme for electron transports. To test the accuracy and efficiency of our dose engine oclMC, we compared dose calculation results of oclMC and gDPM, our previously developed GPU-based MC code, for a 15 MeV electron beam and a 6 MV photon beam on a homogenous water phantom, one slab phantom and one half-slab phantom. Satisfactory agreement was observed in all the cases. The average dose differences within 10% isodose line of the maximum dose were 0.48-0.53% for the electron beam cases and 0.15-0.17% for the photon beam cases. In terms of efficiency, our dose engine oclMC was 6-17% slower than gDPM when running both codes on the same NVidia TITAN card due to both different physics particle transport models and different computational environments between CUDA and OpenCL. The cross-platform portability was also validated by successfully running our new dose engine on a set of different compute devices including an Nvidia GPU card, two AMD GPU cards and an Intel CPU card using one or four cores. Computational efficiency among these platforms was compared.

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arXiv2014

A method for real-time volumetric imaging in radiotherapy using single x-ray projection

In this paper, we present a new method to generate an instantaneous volumetric image using a single x-ray projection. To fully extract motion information hidden in projection images, we partitioned a projection image into small patches. We utilized a sparse learning method to automatically select patches that have a high correlation with principal component analysis (PCA) coefficients of a lung motion model. A model that maps the patch intensity to the PCA coefficients is built along with the patch selection process. Based on this model, a measured projection can be used to predict the PCA coefficients, which are further used to generate a motion vector field and hence a volumetric image. We have also proposed an intensity baseline correction method based on the partitioned projection, where the first and the second moments of pixel intensities at a patch in a simulated image are matched with those in a measured image via a linear transformation. The proposed method has been valid in simulated data and real phantom data. The algorithm is able to identify patches that contain relevant motion information, e.g. diaphragm region. It is found that intensity correction step is important to remove the systematic error in the motion prediction. For the simulation case, the sparse learning model reduced prediction error for the first PCA coefficient to 5%, compared to the 10% error when sparse learning is not used. 95th percentile error for the predicted motion vector is reduced from 2.40 mm to 0.92mm. In the phantom case, the predicted tumor motion trajectory is successfully reconstructed with 0.82 mm mean vector field error compared to 1.66 mm error without using the sparse learning method. The algorithm robustness with respect to sparse level, patch size, and existence of diaphragm, as well as computation time, has also been studied.

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arXiv2013

Comprehensive Evaluations of Cone-beam CT dose in Image-guided Radiation Therapy via GPU-based Monte Carlo simulations

Cone beam CT (CBCT) has been widely used for patient setup in image guided radiation therapy (IGRT). Radiation dose from CBCT scans has become a clinical concern. The purposes of this study are 1) to commission a GPU-based Monte Carlo (MC) dose calculation package gCTD for Varian On-Board Imaging (OBI) system and test the calculation accuracy, and 2) to quantitatively evaluate CBCT dose from the OBI system in typical IGRT scan protocols. We first conducted dose measurements in a water phantom. X-ray source model parameters used in gCTD are obtained through a commissioning process. gCTD accuracy is demonstrated by comparing calculations with measurements in water and in CTDI phantoms. 25 brain cancer patients are used to study dose in a standard-dose head protocol, and 25 prostate cancer patients are used to study dose in pelvis protocol and pelvis spotlight protocol. Mean dose to each organ is calculated. Mean dose to 2% voxels that have the highest dose is also computed to quantify the maximum dose. It is found that the mean dose value to an organ varies largely among patients. Moreover, dose distribution is highly non-homogeneous inside an organ. The maximum dose is found to be 1~3 times higher than the mean dose depending on the organ, and is up to 8 times higher for the entire body due to the very high dose region in bony structures. High computational efficiency has also been observed in our studies, such that MC dose calculation time is less than 5 min for a typical case.

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arXiv2013

The fixed-point iteration method for IMRT optimization with truncated dose deposition coefficient matrix

In the treatment plan optimization for intensity modulated radiation therapy (IMRT), dose-deposition coefficient (DDC) matrix is often pre-computed to parameterize the dose contribution to each voxel in the volume of interest from each beamlet of unit intensity. However, due to the limitation of computer memory and the requirement on computational efficiency, in practice matrix elements of small values are usually truncated, which inevitably compromises the quality of the resulting plan. A fixed-point iteration scheme has been applied in IMRT optimization to solve this problem, which has been reported to be effective and efficient based on the observations of the numerical experiments. In this paper, we aim to point out the mathematics behind this scheme and to answer the following three questions: 1) whether the fixed-point iteration algorithm converges or not? 2) when it converges, whether the fixed point solution is same as the original solution obtained with the complete DDC matrix? 3) if not the same, whether the fixed point solution is more accurate than the naive solution of the truncated problem obtained without the fixed-point iteration? To answer these questions, we first performed mathematical analysis and deductions using a simplified fluence map optimization (FMO) model. Then we conducted numerical experiments on a head-and-neck patient case using both the simplified and the original FMO model. Both our mathematical analysis and numerical experiments demonstrate that with proper DDC matrix truncation, the fixed-point iteration can converge. Even though the converged solution is not the one that we obtain with the complete DDC matrix, the fixed-point iteration scheme could significantly improve the plan accuracy compared with the solution to the truncated problem obtained without the fixed-point iteration.

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arXiv2013

Effect of Statistical Fluctuation in Monte Carlo Based Photon Beam Dose Calculation on Gamma Index Evaluation

The gamma-index test has been commonly adopted to quantify the degree of agreement between a reference dose distribution and an evaluation dose distribution. Monte Carlo (MC) simulation has been widely used for the radiotherapy dose calculation for both clinical and research purposes. The goal of this work is to investigate both theoretically and experimentally the impact of the MC statistical fluctuation on the gamma-index test when the fluctuation exists in the reference, the evaluation, or both dose distributions. To the first order approximation, we theoretically demonstrated in a simplified model that the statistical fluctuation tends to overestimate gamma-index values when existing in the reference dose distribution and underestimate gamma-index values when existing in the evaluation dose distribution given the original gamma-index is relatively large for the statistical fluctuation. Our numerical experiments using clinical photon radiation therapy cases have shown that 1) when performing a gamma-index test between an MC reference dose and a non-MC evaluation dose, the average gamma-index is overestimated and the passing rate decreases with the increase of the noise level in the reference dose; 2) when performing a gamma-index test between a non-MC reference dose and an MC evaluation dose, the average gamma-index is underestimated when they are within the clinically relevant range and the passing rate increases with the increase of the noise level in the evaluation dose; 3) when performing a gamma-index test between an MC reference dose and an MC evaluation dose, the passing rate is overestimated due to the noise in the evaluation dose and underestimated due to the noise in the reference dose. We conclude that the gamma-index test should be used with caution when comparing dose distributions computed with Monte Carlo simulation.

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arXiv2013

A Contour-Guided Deformable Image Registration Algorithm for Adaptive Radiotherapy

In adaptive radiotherapy, deformable image registration is often conducted between the planning CT and treatment CT (or cone beam CT) to generate a deformation vector field (DVF) for dose accumulation and contour propagation. The auto propagated contours on the treatment CT may contain relatively large errors, especially in low contrast regions. A clinician inspection and editing of the propagated contours are frequently needed. The edited contours are able to meet the clinical requirement for adaptive therapy; however, the DVF is still inaccurate and inconsistent with the edited contours. The purpose of this work is to develop a contour-guided deformable image registration (CG-DIR) algorithm to improve the accuracy and consistency of the DVF for adaptive radiotherapy. Incorporation of the edited contours into the registration algorithm is realized by regularizing the objective function of the original demons algorithm with a term of intensity matching between the delineated structures set pairs. The CG-DIR algorithm is implemented on computer graphics processing units (GPUs) by following the original GPU-based demons algorithm computation framework [Gu et al, Phys Med Biol. 55(1): 207-219, 2010]. The performance of CG-DIR is evaluated on five clinical head-and-neck and one pelvic cancer patient data. It is found that compared with the original demons, CG-DIR improves the accuracy and consistency of the DVF, while retaining similar high computational efficiency.

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arXiv2012

Extracting respiratory signals from thoracic cone beam CT projections

Patient respiratory signal associated with the cone beam CT (CBCT) projections is important for lung cancer radiotherapy. In contrast to monitoring an external surrogate of respiration, such signal can be extracted directly from the CBCT projections. In this paper, we propose a novel local principle component analysis (LPCA) method to extract the respiratory signal by distinguishing the respiration motion-induced content change from the gantry rotation-induced content change in the CBCT projections. The LPCA method is evaluated by comparing with three state-of-the-art projection-based methods, namely, the Amsterdam Shroud (AS) method, the intensity analysis (IA) method, and the Fourier-transform based phase analysis (FT-p) method. The clinical CBCT projection data of eight patients, acquired under various clinical scenarios, were used to investigate the performance of each method. We found that the proposed LPCA method has demonstrated the best overall performance for cases tested and thus is a promising technique for extracting respiratory signal. We also identified the applicability of each existing method.

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arXiv2012

A Multi-Criteria Framework with Voxel-Dependent Parameters for Radiotherapy Treatment Plan Optimization

In a treatment plan optimization problem for radiotherapy, a clinically acceptable plan is usually generated by an optimization process with weighting factors or reference doses adjusted for organs. Recent discoveries indicate that adjusting parameters associated with each voxel may lead to better plan quality. However, it is still unclear regarding the mathematical reasons behind it. To answer questions related to this problem, we establish in this work a new mathematical framework equipped with two theorems. The new framework clarifies the different consequences of adjusting organ-dependent and voxel-dependent parameters for the treatment plan optimization of radiation therapy, as well as the different effects of adjusting weighting factors versus reference doses in the optimization process. The main discoveries are threefold: 1) While in the organ-based model the selection of the objective function has an impact on the quality of the optimized plans, this is no longer an issue for the voxel-based model since the entire Pareto surface could be generated regardless the specific form of the objective function as long as it satisfies certain mathematical conditions; 2) A larger Pareto surface is explored by adjusting voxel-dependent parameters than by adjusting organ-dependent parameters, possibly allowing for the generation of plans with better trade-offs among different clinical objectives; 3) Adjusting voxel weighting factors is preferred to adjusting the voxel reference doses since the Pareto optimality can be maintained.

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arXiv2012

A GPU Tool for Efficient, Accurate, and Realistic Simulation of Cone Beam CT Projections

Simulation of x-ray projection images plays an important role in cone beam CT (CBCT) related research projects. A projection image contains primary signal, scatter signal, and noise. It is computationally demanding to perform accurate and realistic computations for all of these components. In this work, we develop a package on GPU, called gDRR, for the accurate and efficient computations of x-ray projection images in CBCT under clinically realistic conditions. The primary signal is computed by a tri-linear ray-tracing algorithm. A Monte Carlo (MC) simulation is then performed, yielding the primary signal and the scatter signal, both with noise. A denoising process is applied to obtain a smooth scatter signal. The noise component is then obtained by combining the difference between the MC primary and the ray-tracing primary signals, and the difference between the MC simulated scatter and the denoised scatter signals. Finally, a calibration step converts the calculated noise signal into a realistic one by scaling its amplitude. For a typical CBCT projection with a poly-energetic spectrum, the calculation time for the primary signal is 1.2~2.3 sec, while the MC simulations take 28.1~95.3 sec. Computation time for all other steps is negligible. The ray-tracing primary signal matches well with the primary part of the MC simulation result. The MC simulated scatter signal using gDRR is in agreement with EGSnrc results with a relative difference of 3.8%. A noise calibration process is conducted to calibrate gDRR against a real CBCT scanner. The calculated projections are accurate and realistic, such that beam-hardening artifacts and scatter artifacts can be reproduced using the simulated projections. The noise amplitudes in the CBCT images reconstructed from the simulated projections also agree with those in the measured images at corresponding mAs levels.

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arXiv2012

CT to Cone-beam CT Deformable Registration With Simultaneous Intensity Correction

Computed tomography (CT) to cone-beam computed tomography (CBCT) deformable image registration (DIR) is a crucial step in adaptive radiation therapy. Current intensity-based registration algorithms, such as demons, may fail in the context of CT-CBCT DIR because of inconsistent intensities between the two modalities. In this paper, we propose a variant of demons, called Deformation with Intensity Simultaneously Corrected (DISC), to deal with CT-CBCT DIR. DISC distinguishes itself from the original demons algorithm by performing an adaptive intensity correction step on the CBCT image at every iteration step of the demons registration. Specifically, the intensity correction of a voxel in CBCT is achieved by matching the first and the second moments of the voxel intensities inside a patch around the voxel with those on the CT image. It is expected that such a strategy can remove artifacts in the CBCT image, as well as ensuring the intensity consistency between the two modalities. DISC is implemented on computer graphics processing units (GPUs) in compute unified device architecture (CUDA) programming environment. The performance of DISC is evaluated on a simulated patient case and six clinical head-and-neck cancer patient data. It is found that DISC is robust against the CBCT artifacts and intensity inconsistency and significantly improves the registration accuracy when compared with the original demons.

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arXiv2012

Optimal Surface Marker Locations for Tumor Motion Estimation in Lung Cancer Radiotherapy

Using fiducial markers on patient's body surface to predict the tumor location is a widely used approach in lung cancer radiotherapy. The purpose of this work is to propose an algorithm that automatically identifies a sparse set of locations on the patient's surface with the optimal prediction power for the tumor motion. The sparse selection of markers on the external surface and the assumed linear relationship between the marker motion and the internal tumor motion are represented by a prediction matrix. Such a matrix is determined by solving an optimization problem, where the objective function contains a sparsity term that penalizes the number of markers chosen on the patient's surface. The performance of our algorithm has been tested on realistic clinical data of four lung cancer patients. Thoracic 4DCT scans with 10 phases are used for the study. On a reference phase, a grid of points are casted on the patient's surface (except for patient's back) and propagated to other phases via deformable image registration of the corresponding CT images. Tumor locations at each phase are also manually delineated. We use 9 out of 10 phases of the 4DCT images to identify a small group of surface markers that are most correlated with the motion of the tumor, and find the prediction matrix at the same time. The 10th phase is then used to test the accuracy of the prediction. It is found that on average 6 to 7 surface markers are necessary to predict tumor locations with a 3D error of about 1mm. In addition, the selected marker locations lie closely in those areas where surface point motion has a high correlation with the tumor motion. Our method can automatically select sparse locations on patient's external surface and estimate a correlation matrix based on 4DCT, so that the selected surface locations can be used to place fiducial markers to optimally predict internal tumor motions.

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arXiv2012

Cine cone beam CT reconstruction using low-rank matrix factorization: algorithm and a proof-of-princple study

Respiration-correlated CBCT, commonly called 4DCBCT, provide respiratory phase-resolved CBCT images. In many clinical applications, it is more preferable to reconstruct true 4DCBCT with the 4th dimension being time, i.e., each CBCT image is reconstructed based on the corresponding instantaneous projection. We propose in this work a novel algorithm for the reconstruction of this truly time-resolved CBCT, called cine-CBCT, by effectively utilizing the underlying temporal coherence, such as periodicity or repetition, in those cine-CBCT images. Assuming each column of the matrix $\bm{U}$ represents a CBCT image to be reconstructed and the total number of columns is the same as the number of projections, the central idea of our algorithm is that the rank of $\bm{U}$ is much smaller than the number of projections and we can use a matrix factorization form $\bm{U}=\bm{L}\bm{R}$ for $\bm{U}$. The number of columns for the matrix $\bm{L}$ constraints the rank of $\bm{U}$ and hence implicitly imposing a temporal coherence condition among all the images in cine-CBCT. The desired image properties in $\bm{L}$ and the periodicity of the breathing pattern are achieved by penalizing the sparsity of the tight wavelet frame transform of $\bm{L}$ and that of the Fourier transform of $\bm{R}$, respectively. A split Bregman method is used to solve the problem. In this paper we focus on presenting this new algorithm and showing the proof of principle using simulation studies on an NCAT phantom.

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