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

Alessandro Perelli1, Martin S Andersen1

  • 1Department of Applied Mathematics and Computer Science (DTU Compute), Technical University of Denmark, Lyngby 2800, Denmark.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|May 10, 2021
PubMed
Summary
This summary is machine-generated.

This study presents an efficient method for reconstructing multi-material images using spectral computed tomography (CT). The approach optimizes image reconstruction by reducing computational complexity while preserving detailed material information.

Keywords:
convolutional neural networksimage denoisingiterative algorithmsspectral X-ray computed tomographystochastic optimization

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Area of Science:

  • Medical Imaging
  • Computational Imaging
  • Materials Science

Background:

  • Spectral Computed Tomography (CT) allows material concentration estimation using photon energy spectra.
  • Reconstructing multi-material images from spectral CT data is computationally challenging.

Purpose of the Study:

  • To develop an efficient algorithm for solving the maximum-a-posterior (MAP) problem in spectral CT.
  • To enable accurate multi-material image reconstruction for spectral CT applications.

Main Methods:

  • A regularized optimization problem is solved using a plug-in image-denoising function and a randomized second-order method.
  • Newton's step is approximated by sketching the Hessian of the likelihood function to reduce complexity.
  • Non-uniform block sub-sampling of the Hessian and inexact conjugate gradient updates are employed.

Main Results:

  • The proposed method efficiently reconstructs multi-material images from spectral CT data.
  • Numerical and experimental results demonstrate the effectiveness of the approach for material decomposition.
  • The method retains complex prior structures from data-driven regularizers.

Conclusions:

  • The developed randomized second-order method offers an efficient solution for spectral CT material decomposition.
  • This technique enhances the capability of spectral CT for quantitative material analysis.
  • The study contributes to synergistic tomographic image reconstruction advancements.