Regularization by Denoising Sub-sampled Newton Method for Spectral CT Multi-Material Decomposition

TL;DR

This paper introduces a novel regularization technique using denoising within a sub-sampled Newton framework to improve spectral CT multi-material decomposition, balancing computational efficiency and complex prior modeling.

Contribution

It proposes a new randomized second order method with a plug-in denoising regularizer for spectral CT, reducing complexity while preserving prior information.

Findings

Effective spectral CT material decomposition demonstrated

Reduced computational complexity with sketching and inexact updates

Numerical and experimental validation of the method

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 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.