Fast solver for some computational imaging problems: A regularized weighted least-squares approach

Bo Zhang (1) , Sherif Makram-Ebeid (1) , Raphael Prevost (2, 1) , Guillaume Pizaine (1)

1 Medisys - MedisysResearch Lab
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

In this paper we propose to solve a range of computational imaging problems under a unified perspective of a regularized weighted least-squares (RWLS) framework. These problems include data smoothing and completion, edge-preserving filtering, gradient-vector flow estimation, and image registration. Although originally very different, they are special cases of the RWLS model using different data weightings and regularization penalties. Numerically, we propose a reconditioned conjugate gradient scheme which is particularly efficient in solving RWLS problems. We provide a detailed analysis of the system conditioning justifying our choice of the preconditioner that improves the convergence. This numerical solver, which is simple, scalable and parallelizable, is found to outperform most of the existing schemes for these imaging problems in terms of convergence rate. Copyright © 2014 Elsevier Inc. All rights reserved. Electronic version of this work can be found by using the following DOI: 10.1016/j.dsp.2014.01.007

Mots clés: Regularized weighted least-squares; Preconditioned conjugate gradient; Preconditioning; Condition number

Domaines: Imagerie médicale; Traitement des images [eess.IV]; Traitement du signal et de l'image [eess.SP]

Bo Zhang, Sherif Makram-Ebeid, Raphael Prevost, Guillaume Pizaine. Fast solver for some computational imaging problems: A regularized weighted least-squares approach. Digital Signal Processing, 2014, 27, pp.107-118. ⟨10.1016/j.dsp.2014.01.007⟩. ⟨hal-01097421⟩