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

Alessandro Perelli, Martin S. Andersen

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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
Issue number2200
Early online date10 May 2021
Publication statusPublished - 28 Jun 2021


  • convolutional neural networks
  • image denoising
  • iterative algorithms
  • spectral X-ray computed tomography
  • stochastic optimization

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)


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