Minimisation and Parameter Estimation in Image Restoration Variational Models with ℓ<sub>1</sub>-Constraints
Year: 2018
East Asian Journal on Applied Mathematics, Vol. 8 (2018), Iss. 1 : pp. 44–69
Abstract
Minimisation of the total variation regularisation for linear operators under $ℓ_1$-constraints applied to image restoration is considered, and relationships between the Lagrange multiplier for a constrained model and the regularisation parameter in an unconstrained model are established. A constrained $ℓ_1$-problem reformulated as a separable convex problem is solved by the alternating direction method of multipliers that includes two sequences, converging to a restored image and the “optimal" regularisation parameter. This allows blurry images to be recovered, with a simultaneous estimation of the regularisation parameter. The noise level parameter is estimated, and numerical experiments illustrate the efficiency of the new approach.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.210117.060817a
East Asian Journal on Applied Mathematics, Vol. 8 (2018), Iss. 1 : pp. 44–69
Published online: 2018-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Parameter selection $ℓ_1$-Constraints alternating direction method of multipliers impulsive noise image processing.