Multiresolution image domain sketching for inverse imaging problems

Alessandro Perelli; Carola-Bibiane  Schönlieb; Matthias Ehrhardt

Abstract

An important challenge in high-dimensional inverse problems such as Computed Tomography (CT) is developing iterative solvers to find the accurate solution of regularized optimization with reduced computational cost. In this work we propose an efficient method to solve such a problem via saddle point optimization and constructing a family of deterministic multiresolution operators that we call image domain sketches. We develop a stochastic gradient algorithm (ImaSk) to solve the saddle point problem that uses at each iteration operators at different resolutions selected through a uniform or non-uniform discrete probability distribution. We demonstrate that the algorithm is converging for strongly convex regularization functions. Numerical simulations on CT show that the proposed method is effective in reducing the computational time to reach the modelled solution compared to the full resolution-based solvers.

Original language	English
Publication status	Published - Jun 2023
Event	SIAM Conference on Optimization (OP23): MS181 Optimization for Image Reconstruction - Part I of II - The Sheraton Grand Seattle, Seattle, United States Duration: 31 May 2023 → 3 Jun 2023 https://www.siam.org/conferences/cm/conference/op23

Conference

Conference	SIAM Conference on Optimization (OP23)
Country/Territory	United States
City	Seattle
Period	31/05/23 → 3/06/23
Internet address	https://www.siam.org/conferences/cm/conference/op23

Keywords

imaging/CT MRI
optimization
multiresolution

Access to Document

https://meetings.siam.org/sess/dsp_talk.cfm?p=128369

Cite this

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title = "Multiresolution image domain sketching for inverse imaging problems",

abstract = "An important challenge in high-dimensional inverse problems such as Computed Tomography (CT) is developing iterative solvers to find the accurate solution of regularized optimization with reduced computational cost. In this work we propose an efficient method to solve such a problem via saddle point optimization and constructing a family of deterministic multiresolution operators that we call image domain sketches. We develop a stochastic gradient algorithm (ImaSk) to solve the saddle point problem that uses at each iteration operators at different resolutions selected through a uniform or non-uniform discrete probability distribution. We demonstrate that the algorithm is converging for strongly convex regularization functions. Numerical simulations on CT show that the proposed method is effective in reducing the computational time to reach the modelled solution compared to the full resolution-based solvers.",

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author = "Alessandro Perelli and Carola-Bibiane Sch{\"o}nlieb and Matthias Ehrhardt",

year = "2023",

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language = "English",

note = "SIAM Conference on Optimization (OP23) : MS181 Optimization for Image Reconstruction - Part I of II ; Conference date: 31-05-2023 Through 03-06-2023",

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TY - CONF

T1 - Multiresolution image domain sketching for inverse imaging problems

AU - Perelli, Alessandro

AU - Schönlieb, Carola-Bibiane

AU - Ehrhardt, Matthias

PY - 2023/6

Y1 - 2023/6

N2 - An important challenge in high-dimensional inverse problems such as Computed Tomography (CT) is developing iterative solvers to find the accurate solution of regularized optimization with reduced computational cost. In this work we propose an efficient method to solve such a problem via saddle point optimization and constructing a family of deterministic multiresolution operators that we call image domain sketches. We develop a stochastic gradient algorithm (ImaSk) to solve the saddle point problem that uses at each iteration operators at different resolutions selected through a uniform or non-uniform discrete probability distribution. We demonstrate that the algorithm is converging for strongly convex regularization functions. Numerical simulations on CT show that the proposed method is effective in reducing the computational time to reach the modelled solution compared to the full resolution-based solvers.

AB - An important challenge in high-dimensional inverse problems such as Computed Tomography (CT) is developing iterative solvers to find the accurate solution of regularized optimization with reduced computational cost. In this work we propose an efficient method to solve such a problem via saddle point optimization and constructing a family of deterministic multiresolution operators that we call image domain sketches. We develop a stochastic gradient algorithm (ImaSk) to solve the saddle point problem that uses at each iteration operators at different resolutions selected through a uniform or non-uniform discrete probability distribution. We demonstrate that the algorithm is converging for strongly convex regularization functions. Numerical simulations on CT show that the proposed method is effective in reducing the computational time to reach the modelled solution compared to the full resolution-based solvers.

KW - imaging/CT MRI

KW - optimization

KW - multiresolution

M3 - Abstract

T2 - SIAM Conference on Optimization (OP23)

Y2 - 31 May 2023 through 3 June 2023