Efficient edge-preserving methods for dynamic inverse problems

TL;DR

This paper introduces efficient, regularized iterative methods for solving large-scale dynamic inverse problems, improving accuracy and computational efficiency in applications like CT, deblurring, and PAT.

Contribution

It develops a novel majorization-minimization based iterative framework with automatic regularization parameter selection for dynamic inverse problems.

Findings

Effective in limited-angle CT reconstruction

Improves space-time image deblurring accuracy

Applicable to photoacoustic tomography

Abstract

We consider efficient methods for computing solutions to dynamic inverse problems, where both the quantities of interest and the forward operator (measurement process) may change at different time instances but we want to solve for all the images simultaneously. We are interested in large-scale ill-posed problems that are made more challenging by their dynamic nature and, possibly, by the limited amount of available data per measurement step. To remedy these difficulties, we apply regularization methods that enforce simultaneous regularization in space and time (such as edge enhancement at each time instant and proximity at consecutive time instants) and achieve this with low computational cost and enhanced accuracy. More precisely, we develop iterative methods based on a majorization-minimization (MM) strategy with quadratic tangent majorant, which allows the resulting least squares problem to be solved with a generalized Krylov subspace (GKS) method; the regularization parameter can be defined automatically and efficiently at each iteration. Numerical examples from a wide range of applications, such as limited-angle computerized tomography (CT), space-time image deblurring, and photoacoustic tomography (PAT), illustrate the effectiveness of the described approaches.