PURPOSE:Total Variation (TV) minimization algorithm is a classical compressed sensing (CS) based iterative image reconstruction algorithm that can accurately reconstruct images from sparse-view projections in computed tomography (CT). However, the system matrix used in the algorithm is often too large to be stored in computer memory. The purpose of this study is to investigate a new TV algorithm based on image rotation and without system matrix to avoid the memory requirement of system matrix. METHODS:Without loss of generality, a rotation-based adaptive steepest descent-projection onto convex sets (R-ASD-POCS) algorithm is proposed and tested to solve the TV model in parallel beam CT. Specifically, simulation experiments are performed via the Shepp-Logan, FORBILD and real CT image phantoms are used to verify the inverse-crime capability of the algorithm and evaluate the sparse reconstruction capability and the noise suppression performance of the algorithm. RESULTS:Experimental results show that the algorithm can achieve inverse-crime, accurate sparse reconstruction and thus accurately reconstruct images from noisy projections. Compared with the classical ASD-POCS algorithm, the new algorithm may yield the similar image reconstruction accuracy without use of the huge system matrix, which saves the computational memory space significantly. Additionally, the results also show that R-ASD-POCS algorithm is faster than ASD-POCS. CONCLUSIONS:The proposed new algorithm can effectively solve the problem of using huge memory in large scale and iterative image reconstruction. Integrating with ASD-POCS frame, this no-system-matrix based scheme may be readily extended and applied to any iterative image reconstructions.

中文翻译：

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一种无系统矩阵的TV最小化图像重建算法

目的：全变差 (TV) 最小化算法是一种经典的基于压缩感知 (CS) 的迭代图像重建算法，可以准确地从计算机断层扫描 (CT) 中的稀疏视图投影重建图像。然而，算法中使用的系统矩阵通常太大而无法存储在计算机内存中。本研究的目的是研究一种新的基于图像旋转且无系统矩阵的TV算法，以避免系统矩阵的内存需求。方法：在不失一般性的前提下，提出并测试了一种基于旋转的自适应最速下降投影到凸集（R-ASD-POCS）算法来求解平行束CT中的TV模型。具体来说，模拟实验是通过 Shepp-Logan 进行的，使用 FORBILD 和真实 CT 图像模型验证算法的反犯罪能力，评估算法的稀疏重建能力和噪声抑制性能。结果：实验结果表明，该算法可以实现反犯罪、准确的稀疏重建，从而准确地从噪声投影中重建图像。与经典的 ASD-POCS 算法相比，新算法无需使用庞大的系统矩阵即可获得相似的图像重建精度，显着节省了计算内存空间。此外，结果还表明 R-ASD-POCS 算法比 ASD-POCS 更快。结论：所提出的新算法可以有效解决大规模图像迭代重建中使用巨大内存的问题。与 ASD-POCS 框架集成，