基于稀疏度的MAP建模的低剂量X射线CT高效重建
Efficient Low Dose X-ray CT Reconstruction through Sparsity-Based MAP Modeling
摘要：
X射线计算机断层扫描（CT）中的超低辐射剂量是一个重要的临床目标，以最大限度地降低致癌风险。压缩感知（CS）能够通过从有限数量的CT投影生成诊断图像来显著降低辐射剂量。然而，传统的基于CS的CT重建通常需要过多的计算时间，这限制了临床实施。在本文中，我们首先证明了一个彻底的分析CT重建通过最大后验目标函数的结果在一个加权压缩感知问题。这种分析使我们能够制定一个低剂量的扇形束和螺旋锥束CT重建。随后，我们提供了一个有效的解决方案，制定CS问题的基础上的快速复合分裂算法潜在的期望最大化（FCSA-LEM）算法。在该方法中，我们使用伪极傅里叶变换作为测量矩阵，以降低计算复杂度;和重组的投影平行射线，以扩大其应用范围的扇形束和螺旋锥束扫描。所提出的加权CS模型中涉及的权重，表示为误差自适应权重（EAW），计算基于CT重建的统计特性，是泊松测量噪声和重组插值误差的函数。仿真结果表明，该方法计算复杂度低，能够快速恢复CT图像，使用EAW可以将重建误差降低一个数量级。在没有数值优化的情况下，在台式计算机上在不到20秒的时间内实现了高质量512 $\times$ 512图像的恢复。
英文摘要：
Ultra low radiation dose in X-ray Computed Tomography (CT) is an important clinical objective in order to minimize the risk of carcinogenesis. Compressed Sensing (CS) enables significant reductions in radiation dose to be achieved by producing diagnostic images from a limited number of CT projections. However, the excessive computation time that conventional CS-based CT reconstruction typically requires has limited clinical implementation. In this paper, we first demonstrate that a thorough analysis of CT reconstruction through a Maximum a Posteriori objective function results in a weighted compressive sensing problem. This analysis enables us to formulate a low dose fan beam and helical cone beam CT reconstruction. Subsequently, we provide an efficient solution to the formulated CS problem based on a Fast Composite Splitting Algorithm-Latent Expected Maximization (FCSA-LEM) algorithm. In the proposed method we use pseudo polar Fourier transform as the measurement matrix in order to decrease the computational complexity; and rebinning of the projections to parallel rays in order to extend its application to fan beam and helical cone beam scans. The weight involved in the proposed weighted CS model, denoted by Error Adaptation Weight (EAW), is calculated based on the statistical characteristics of CT reconstruction and is a function of Poisson measurement noise and rebinning interpolation error. Simulation results show that low computational complexity of the proposed method made the fast recovery of the CT images possible and using EAW reduces the reconstruction error by one order of magnitude. Recovery of a high quality 512$\times$ 512 image was achieved in less than 20 sec on a desktop computer without numerical optimizations.
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