SIAM Journal on Imaging Sciences, Volume 13, Issue 4, Page 1860-1897, January 2020.
X-ray computed tomography (CT) reconstruction from a sparse number of views is a useful way to reduce either the radiation dose or the acquisition time, for example in fixed-gantry CT systems; however, this results in an ill-posed inverse problem whose solution is typically computationally demanding. Approximate message passing (AMP) techniques represent the state of the art for solving undersampling compressed sensing problems with random linear measurements, but there are still not clear solutions on how AMP should be modified and how it performs with real world problems. This paper investigates the question of whether we can employ an AMP framework for real sparse view CT imaging. The proposed algorithm for approximate inference in tomographic reconstruction incorporates a number of advances from within the AMP community, resulting in the denoising generalized approximate message passing CT algorithm (D-GAMP-CT). Specifically, this exploits the use of sophisticated image denoisers to regularize the reconstruction. While in order to reduce the probability of divergence the (Radon) system and the Poisson nonlinear noise model are treated separately, exploiting the existence of efficient preconditioners for the former and the generalized noise modeling in GAMP for the latter. Experiments with simulated and real CT baggage scans confirm that the performance of the proposed algorithm outperforms statistical CT optimization solvers.

中文翻译：

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通过对近似消息传递进行降噪来压缩压缩层析成像

SIAM影像科学杂志，第13卷，第4期，第1860-1897页，2020年1月。
从稀疏视图中进行X射线计算机断层摄影（CT）重建是减少辐射剂量或减少采集时间的有用方法，例如在固定机架CT系统中；但是，这会导致不适定的逆问题，其解决方案通常需要计算。近似消息传递（AMP）技术代表了使用随机线性测量来解决欠采样压缩传感问题的最新技术，但是对于如何修改AMP以及如何解决实际问题，仍然没有明确的解决方案。本文研究了是否可以将AMP框架用于真正的稀疏视图CT成像。断层摄影重建中的近似推理的拟议算法融合了AMP社区内部的许多进步，结果导致去噪广义近似消息通过CT算法（D-GAMP-CT）。具体而言，这利用了复杂的图像降噪器来规范化重建。为了降低发散的可能性，分别对（Radon）系统和Poisson非线性噪声模型进行了处理，同时利用了前者的有效预处理器和后者的GAMP中的广义噪声模型。模拟和实际CT行李扫描的实验证实，所提出算法的性能优于统计CT优化求解器。为了降低发散的可能性，分别对（Radon）系统和Poisson非线性噪声模型进行了处理，同时利用了前者的有效预处理器和后者的GAMP中的广义噪声模型。模拟和实际CT行李扫描的实验证实，所提出算法的性能优于统计CT优化求解器。为了降低发散的可能性，分别对（Radon）系统和Poisson非线性噪声模型进行了处理，同时利用了前者的有效预处理器和后者的GAMP中的广义噪声模型。模拟和实际CT行李扫描的实验证实，所提出算法的性能优于统计CT优化求解器。