Perelli Alessandro, Andersen Martin S
Department of Applied Mathematics and Computer Science (DTU Compute), Technical University of Denmark, Lyngby 2800, Denmark.
Philos Trans A Math Phys Eng Sci. 2021 Jun 28;379(2200):20200191. doi: 10.1098/rsta.2020.0191. Epub 2021 May 10.
Spectral Computed Tomography (CT) is an emerging technology that enables us to estimate the concentration of basis materials within a scanned object by exploiting different photon energy spectra. In this work, we aim at efficiently solving a model-based maximum-a-posterior problem to reconstruct multi-materials images with application to spectral CT. In particular, we propose to solve a regularized optimization problem based on a plug-in image-denoising function using a randomized second order method. By approximating the Newton step using a sketching of the Hessian of the likelihood function, it is possible to reduce the complexity while retaining the complex prior structure given by the data-driven regularizer. We exploit a non-uniform block sub-sampling of the Hessian with inexact but efficient conjugate gradient updates that require only Jacobian-vector products for denoising term. Finally, we show numerical and experimental results for spectral CT materials decomposition. This article is part of the theme issue 'Synergistic tomographic image reconstruction: part 1'.
光谱计算机断层扫描(CT)是一项新兴技术,它通过利用不同的光子能谱,使我们能够估计扫描对象内基础材料的浓度。在这项工作中,我们旨在高效地解决一个基于模型的最大后验问题,以重建多材料图像并应用于光谱CT。具体而言,我们建议使用随机二阶方法来解决基于插件式图像去噪函数的正则化优化问题。通过使用似然函数的海森矩阵草图来近似牛顿步长,可以在保留数据驱动正则化器给出的复杂先验结构的同时降低复杂度。我们利用海森矩阵的非均匀块子采样,并通过不精确但高效的共轭梯度更新,该更新仅需要用于去噪项的雅可比向量积。最后,我们展示了光谱CT材料分解的数值和实验结果。本文是主题问题“协同断层图像重建:第1部分”的一部分。