Regularized Newton Sketch by Denoising Score Matching for Computed Tomography Reconstruction

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Abstract

In this work we aim at efficiently solving a model-based maximum-a-posterior (MAP) image reconstruction with application to low-dose transmission X-ray Computed tomography (CT). We propose to solve the regularized optimization problem by a randomized second order method called Newton iterative Hessian sketching for the Poisson likelihood function and to design a regularization term for the MAP problem exploiting the denoising score framework. By approximating the Newton step using a partial Hessian sketch only for the data fit term, it is possible to reduce the complexity by dimensionality reduction while retaining the complex prior structure by a data-driven regularizer. This work shows how to use partial Netwon sketch with denoising score matching and how to efficiently compute the gradient and the Hessian of the likelihood and regularizer. Finally, we show an example for monoenergetic X-ray CT reconstruction.
Original languageEnglish
Title of host publicationProceedings of the Workshop on Signal Processing with Adaptive Sparse Structured Representations
Number of pages2
Publication date2019
Publication statusPublished - 2019
Event2019 Workshop on Signal Processing with Adaptive Sparse Structured Representations - INP-ENSEEIHT, Toulouse, France
Duration: 1 Jul 20194 Jul 2019
http://www.spars-workshop.org/

Conference

Conference2019 Workshop on Signal Processing with Adaptive Sparse Structured Representations
LocationINP-ENSEEIHT
CountryFrance
CityToulouse
Period01/07/201904/07/2019
Internet address

Cite this

Perelli, A., & Andersen, M. S. (2019). Regularized Newton Sketch by Denoising Score Matching for Computed Tomography Reconstruction. In Proceedings of the Workshop on Signal Processing with Adaptive Sparse Structured Representations