Regularization by denoising sub-sampled Newton method for spectral CT multi-material decomposition

Alessandro Perelli, Martin S Andersen

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Abstract

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'.
Original languageEnglish
Article number20200191
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume379
Issue number2200
Number of pages25
ISSN1364-503X
DOIs
Publication statusPublished - 2021

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