Regularization by Denoising Sub-Sampled Newton Method for Spectral CT Multi-Material Decomposition
Abstract
Spectral Computed Tomography (CT) is an emerging technology that enables 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 multimaterials 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).
The implementation of the method and the CT dataset are available here. Matlab code, Dataset
