基于压缩传感理论的锥束CT断层图像重建算法研究
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摘要
计算机断层成像(Computed Tomography，CT)技术通过无损方式获取物体内部结构信息，广泛用于医学辅助诊断、工业无损检测、安全检查等领域。锥束CT体积小，重量轻，移动灵活，可在手术中快速拍片、定位，广泛用于介入手术治疗。受圆轨道几何扫描结构限制，锥束CT无法获取完备投影数据，制约了锥束CT成像质量。近年提出的压缩感知理论是一种信号高度不完备线性测量的高精确重建技术。在锥束CT图像重建领域，压缩感知理论利用图像的稀疏性先验信息，可从少视角投影数据中精确恢复原始图像。本文基于压缩感知理论，围绕重建精度、收敛速度和计算效率等问题展开研究工作，重点研究了基于FDK的反投影权重算法、基于投影收缩的压缩感知算法、快速自适应共轭梯度投影算法和锥束CT重建并行加速算法，其成果如下：
针对锥束CT系统锥角增大而导致的锥束伪影严重的问题，提出了一种基于FDK的反投影权重锥束CT重建算法(back projection weighted FDK，BPW-FDK)。分析了圆扫描轨迹远端伪影的成因，针对圆周扫描阴影区域导致的Radon空间数据缺失，提出了一种距离变量的反投影权重函数，并将其作为约束条件引入到FDK算法中，实现扫描轨迹远端区域的数据补偿，扩大图像重建区域。与Parker-FDK算法相比，BPW-FDK算法重建图像在目标区域的归一化均方距离判据d和归一化平均绝对距离判据r均下降了50%以上，信噪比提高了5db。
针对锥束CT成像系统中不完全投影数据重建问题，提出了一种基于投影收缩的压缩感知锥束CT短扫描重建算法(Projection-Contraction Barzilari-Borwein，PCBB)。针对BB梯度投影算法的非单调收敛，分析投影收缩法的预测校正特性，将校正过程引入压缩感知图像重建算法中，结合目标函数下降方向和凸集投影下降方向，对BB梯度投影算法进行校正，改善BB梯度投影算法的非单调特性。仿真结果表明，在25个采样角度下，PCBB算法重建图像的信噪比值比ASD-POCS算法、PC算法、GPBB算法的重建结果分别高出9.4870db、9.8027db、3.6159db。
针对锥束CT成像系统中压缩感知算法最速下降法收敛缓慢问题，提出了一种快速自适应共轭梯度压缩感知锥束CT重建算法(adaptive stepsize congjuategradient, ASCG)。利用Lipschitz连续性求出下降步长，然后使用共轭梯度下降法迭代计算，最后采用联合代数重建算法更新重建图像。在每次迭代过程中自适应调整梯度下降步长，进一步加快重建算法的收敛速度。ASCG算法能够有效抑制条状伪影，极大提高少量投影数据时重建图像质量。在40投影角度下，ASCG算法重建结果的相对误差为0.1%，比GPBB算法重建结果的相对误差提高了一个数量级。
锥束CT图像重建的计算复杂度与被重建体数据量N、投影视图个数M的乘积成正比，CPU架构的锥束CT图像重建时间往往达到几十分钟，难以满足实时成像要求。针对锥束CT图像重建时间过长这一瓶颈问题，提出了高度优化的基于GPU的Parker-FDK算法和联合代数重建算法(Simultaneous AlgebraicReconstruction Technique，SART)。基于CUDA架构的Parker-FDK算法充分利用以下技术：(1)优化使用线程块大小；(2)提高常量存储器和共享存储器的重复利用率；(3)使用纹理存储器的线性插值提高计算效率；(4)使用多GPU进一步提高加速比。基于CUDA的SART代码实现：(1)基于射线驱动的正投影技术，使用纹理存储器三线性插值技术；(2)基于体素驱动的反投影技术，使用共享存储器减少冗余计算。实验结果表明，基于CUDA架构的Parker-FDK算法和SART算法的时间性能得到极大提升：Parker-FDK算法的重建时间减少为0.33s；与CPU相比，基于CUDA架构的SART算法加速比约为100倍。
Computed tomography (CT) technique can get the internal information through anon-destructive way and has been widely used in a large number of applications inmedical diagnosis, industrial non-destructive detection and other fields. Because of itssmall size, light weight, mobility and flexiblity, cone-beam CT is extensively appliedto interventional surgery. However, cone-beam CT can not get sufficient projectiondata for exact reconstruction due to its sparse views. Thus the quality of thereconstructed image is not satisfied. Recent developments in compressed sensing haveenabled an accurate cone beam computed tomography (CBCT) reconstruction fromhighly undersampled projections. In this dissertation, we concentrate on thebackprojection weighted FDK algorithm, projection contraction based compressedsensing algorithm, a fast adaptive conjugate gradient projection algorithm to improvethe reconstruction accuracy and convergence speed. GPU is used to accelerate theimage reconstruction. The results are as follows:
Cone beam artifacts increase along with the larger cone angle because thescanning trajectory of cone beam does not sufficiently satisfy data conditions. Aimedat the characteristics of missing data in Radon space, we propose a BackprojectionWeighted-FDK (BPW-FDK) algorithm for CBCT. A new backprojection weight ispresented to compensate for the missing data away from the rotating track forreconstruction region expansion. The images reconstructed from simulated noiselessprojections, projections with noise, and real projections from an internally developed3D scanner show that the proposed algorithm is able to sufficiently suppressartifacts away from the rotating track for large cone angle and provide more homogeneous image contrast. Its accuracy and speed make BPW-FDK algorithmsuitable for image reconstruction of real large CBCT.
To solve the problem of image reconstruction of incomplete projection data fromcone-beam CT, a novel cone-beam CT reconstruction algorithm based onprojection-contraction method was proposed. Aiming at the non-monotonicconvergence of Gradient-Projection Barzilari-Borwein algorithm (GPBB), thepredictor-corrector feature of projection-contraction method was analyzed and wasincorporated into compressed sensing image reconstruction algorithm. The objectivefunction descent direction and the projection onto convex sets descent direction werecombined to correct the results of GPBB algorithm to improve the non-monotonicconvergence of GPBB algorithm. The experiments were conducted on simulatedprojection data and phantom scanning data. The simulated results show that, for25sampling angles, signal-to-noise ratio of images reconstructed by PCBB algorithm is9.4870db,9.8027db,3.6159db higher than those of images reconstructed by AdaptiveSteepest Descent-Projection Onto Convex Sets algorithm, projection contractionalgorithm and GPBB algorithm, respectively. The results of Phantom indicate thateven when a small amount of projections are acquired, the new algorithm caneffectively suppress strip artifacts and the reconstructed images show clear edge. Thealgorithm can greatly improve qualify of images reconstructed from few projectiondata.
Recent developments in compressed sensing have enabled an accurate conebeam computed tomography (CBCT) reconstruction from highly undersampledprojections. However, gradient descent commonly used in these reconstructionmethods has a slow convergence speed. In this paper, we propose a novel CBCTreconstruction algorithm based on adaptive stepsize conjugate gradient (ASCG)method, which overcomes the drawback of the gradient descent methods. The CBCTimages are reconstructed by minimizing an objective function consisting of a datafidelity term and a TV-norm regularization term. While the data fidelity term uses l2norm to enforce the similarities between the measured projection data with theforward projections of reconstructed images, the penalty term uses Total variation(TV)-norm to enforce the piecewise constant property of the unknown object. Theobject function is minimized by conjugate gradient projection with the stepsizeanalytically calculated and adaptively changed at each iteration. The line searchtechnique is avoided to lessen the computation time. The Forbild numerical phantom is used to evaluate the performance of ASCG. Image relative error of reconstructedimages and computation efficiency were assessed and the behavior of ASCG arecompared with simultaneous algebraic reconstruction technique (SART), gradientprojection Barzilai-Borwein (GPBB) and another conjugate gradient projection usingfixed stepsize which is referred to FSCG. Under the condition of50-view projections,the ASCG algorithm showed convergence about600iterations whereas otheralgorithms need more than1000iterations to reconstruct the Forbild phantom image.For the same number of iteration, the computation time of ASCG is less than half ofthose of GPBB algorithm. we propose a novel adaptive stepsize conjugate gradientprojection algorithm for sparse-view CBCT reconstruction. Compared to GPBBalgorithm, ASCG algorithm has better performance both in convergence speed andreconstruction accuracy. These advantages have been demonstrated on Forbildphantom studies.
To accelerate the Parker-FDK algorithm and SART for speedy and quality CTreconstruction by exploiting CUDA-enabled GPU, these techniques are proposed:(1)optimizing thread block size,(2) maximizing data reuse on constant memory andshared memory,(3) exploiting texture memory interpolation capability to increaseefficiency, and (4) using multiply GPUs. Two core techniques are proposed to useSART into the CUDA architecture:(1) a ray-driven projection along with hardwareinterpolation, and (2) a voxel-driven back-projection that can avoid redundantcomputation by combining CUDA shared memory. Extensive experimentsdemonstrate the proposed techniques can provide faster reconstruction with satisfiedimage quality.
针对锥束CT系统锥角增大而导致的锥束伪影严重的问题，提出了一种基于FDK的反投影权重锥束CT重建算法(back projection weighted FDK，BPW-FDK)。分析了圆扫描轨迹远端伪影的成因，针对圆周扫描阴影区域导致的Radon空间数据缺失，提出了一种距离变量的反投影权重函数，并将其作为约束条件引入到FDK算法中，实现扫描轨迹远端区域的数据补偿，扩大图像重建区域。与Parker-FDK算法相比，BPW-FDK算法重建图像在目标区域的归一化均方距离判据d和归一化平均绝对距离判据r均下降了50%以上，信噪比提高了5db。
针对锥束CT成像系统中不完全投影数据重建问题，提出了一种基于投影收缩的压缩感知锥束CT短扫描重建算法(Projection-Contraction Barzilari-Borwein，PCBB)。针对BB梯度投影算法的非单调收敛，分析投影收缩法的预测校正特性，将校正过程引入压缩感知图像重建算法中，结合目标函数下降方向和凸集投影下降方向，对BB梯度投影算法进行校正，改善BB梯度投影算法的非单调特性。仿真结果表明，在25个采样角度下，PCBB算法重建图像的信噪比值比ASD-POCS算法、PC算法、GPBB算法的重建结果分别高出9.4870db、9.8027db、3.6159db。
针对锥束CT成像系统中压缩感知算法最速下降法收敛缓慢问题，提出了一种快速自适应共轭梯度压缩感知锥束CT重建算法(adaptive stepsize congjuategradient, ASCG)。利用Lipschitz连续性求出下降步长，然后使用共轭梯度下降法迭代计算，最后采用联合代数重建算法更新重建图像。在每次迭代过程中自适应调整梯度下降步长，进一步加快重建算法的收敛速度。ASCG算法能够有效抑制条状伪影，极大提高少量投影数据时重建图像质量。在40投影角度下，ASCG算法重建结果的相对误差为0.1%，比GPBB算法重建结果的相对误差提高了一个数量级。
锥束CT图像重建的计算复杂度与被重建体数据量N、投影视图个数M的乘积成正比，CPU架构的锥束CT图像重建时间往往达到几十分钟，难以满足实时成像要求。针对锥束CT图像重建时间过长这一瓶颈问题，提出了高度优化的基于GPU的Parker-FDK算法和联合代数重建算法(Simultaneous AlgebraicReconstruction Technique，SART)。基于CUDA架构的Parker-FDK算法充分利用以下技术：(1)优化使用线程块大小；(2)提高常量存储器和共享存储器的重复利用率；(3)使用纹理存储器的线性插值提高计算效率；(4)使用多GPU进一步提高加速比。基于CUDA的SART代码实现：(1)基于射线驱动的正投影技术，使用纹理存储器三线性插值技术；(2)基于体素驱动的反投影技术，使用共享存储器减少冗余计算。实验结果表明，基于CUDA架构的Parker-FDK算法和SART算法的时间性能得到极大提升：Parker-FDK算法的重建时间减少为0.33s；与CPU相比，基于CUDA架构的SART算法加速比约为100倍。
Computed tomography (CT) technique can get the internal information through anon-destructive way and has been widely used in a large number of applications inmedical diagnosis, industrial non-destructive detection and other fields. Because of itssmall size, light weight, mobility and flexiblity, cone-beam CT is extensively appliedto interventional surgery. However, cone-beam CT can not get sufficient projectiondata for exact reconstruction due to its sparse views. Thus the quality of thereconstructed image is not satisfied. Recent developments in compressed sensing haveenabled an accurate cone beam computed tomography (CBCT) reconstruction fromhighly undersampled projections. In this dissertation, we concentrate on thebackprojection weighted FDK algorithm, projection contraction based compressedsensing algorithm, a fast adaptive conjugate gradient projection algorithm to improvethe reconstruction accuracy and convergence speed. GPU is used to accelerate theimage reconstruction. The results are as follows:
Cone beam artifacts increase along with the larger cone angle because thescanning trajectory of cone beam does not sufficiently satisfy data conditions. Aimedat the characteristics of missing data in Radon space, we propose a BackprojectionWeighted-FDK (BPW-FDK) algorithm for CBCT. A new backprojection weight ispresented to compensate for the missing data away from the rotating track forreconstruction region expansion. The images reconstructed from simulated noiselessprojections, projections with noise, and real projections from an internally developed3D scanner show that the proposed algorithm is able to sufficiently suppressartifacts away from the rotating track for large cone angle and provide more homogeneous image contrast. Its accuracy and speed make BPW-FDK algorithmsuitable for image reconstruction of real large CBCT.
To solve the problem of image reconstruction of incomplete projection data fromcone-beam CT, a novel cone-beam CT reconstruction algorithm based onprojection-contraction method was proposed. Aiming at the non-monotonicconvergence of Gradient-Projection Barzilari-Borwein algorithm (GPBB), thepredictor-corrector feature of projection-contraction method was analyzed and wasincorporated into compressed sensing image reconstruction algorithm. The objectivefunction descent direction and the projection onto convex sets descent direction werecombined to correct the results of GPBB algorithm to improve the non-monotonicconvergence of GPBB algorithm. The experiments were conducted on simulatedprojection data and phantom scanning data. The simulated results show that, for25sampling angles, signal-to-noise ratio of images reconstructed by PCBB algorithm is9.4870db,9.8027db,3.6159db higher than those of images reconstructed by AdaptiveSteepest Descent-Projection Onto Convex Sets algorithm, projection contractionalgorithm and GPBB algorithm, respectively. The results of Phantom indicate thateven when a small amount of projections are acquired, the new algorithm caneffectively suppress strip artifacts and the reconstructed images show clear edge. Thealgorithm can greatly improve qualify of images reconstructed from few projectiondata.
Recent developments in compressed sensing have enabled an accurate conebeam computed tomography (CBCT) reconstruction from highly undersampledprojections. However, gradient descent commonly used in these reconstructionmethods has a slow convergence speed. In this paper, we propose a novel CBCTreconstruction algorithm based on adaptive stepsize conjugate gradient (ASCG)method, which overcomes the drawback of the gradient descent methods. The CBCTimages are reconstructed by minimizing an objective function consisting of a datafidelity term and a TV-norm regularization term. While the data fidelity term uses l2norm to enforce the similarities between the measured projection data with theforward projections of reconstructed images, the penalty term uses Total variation(TV)-norm to enforce the piecewise constant property of the unknown object. Theobject function is minimized by conjugate gradient projection with the stepsizeanalytically calculated and adaptively changed at each iteration. The line searchtechnique is avoided to lessen the computation time. The Forbild numerical phantom is used to evaluate the performance of ASCG. Image relative error of reconstructedimages and computation efficiency were assessed and the behavior of ASCG arecompared with simultaneous algebraic reconstruction technique (SART), gradientprojection Barzilai-Borwein (GPBB) and another conjugate gradient projection usingfixed stepsize which is referred to FSCG. Under the condition of50-view projections,the ASCG algorithm showed convergence about600iterations whereas otheralgorithms need more than1000iterations to reconstruct the Forbild phantom image.For the same number of iteration, the computation time of ASCG is less than half ofthose of GPBB algorithm. we propose a novel adaptive stepsize conjugate gradientprojection algorithm for sparse-view CBCT reconstruction. Compared to GPBBalgorithm, ASCG algorithm has better performance both in convergence speed andreconstruction accuracy. These advantages have been demonstrated on Forbildphantom studies.
To accelerate the Parker-FDK algorithm and SART for speedy and quality CTreconstruction by exploiting CUDA-enabled GPU, these techniques are proposed:(1)optimizing thread block size,(2) maximizing data reuse on constant memory andshared memory,(3) exploiting texture memory interpolation capability to increaseefficiency, and (4) using multiply GPUs. Two core techniques are proposed to useSART into the CUDA architecture:(1) a ray-driven projection along with hardwareinterpolation, and (2) a voxel-driven back-projection that can avoid redundantcomputation by combining CUDA shared memory. Extensive experimentsdemonstrate the proposed techniques can provide faster reconstruction with satisfiedimage quality.
引文
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