Volume 8, Issue 1
Minimisation and Parameter Estimation in Image Restoration Variational Models with ℓ1-Constraints

M. Tao

East Asian J. Appl. Math., 8 (2018), pp. 44-69.

Published online: 2018-02

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  • Abstract

Minimisation of the total variation regularisation for linear operators under ℓ1-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 ℓ1-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.

  • Keywords

Parameter selection ell_1-Constraints alternating direction method of multipliers impulsive noise image processing

  • AMS Subject Headings

68U10 65J22 65K10 90C25

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COPYRIGHT: © Global Science Press

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@Article{EAJAM-8-44, author = {M. Tao}, title = {Minimisation and Parameter Estimation in Image Restoration Variational Models with ℓ1-Constraints}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {8}, number = {1}, pages = {44--69}, abstract = {

Minimisation of the total variation regularisation for linear operators under ℓ1-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 ℓ1-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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.210117.060817a}, url = {http://global-sci.org/intro/article_detail/eajam/10884.html} }
TY - JOUR T1 - Minimisation and Parameter Estimation in Image Restoration Variational Models with ℓ1-Constraints AU - M. Tao JO - East Asian Journal on Applied Mathematics VL - 1 SP - 44 EP - 69 PY - 2018 DA - 2018/02 SN - 8 DO - http://dor.org/10.4208/eajam.210117.060817a UR - https://global-sci.org/intro/article_detail/eajam/10884.html KW - Parameter selection KW - ell_1-Constraints KW - alternating direction method of multipliers KW - impulsive noise KW - image processing AB -

Minimisation of the total variation regularisation for linear operators under ℓ1-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 ℓ1-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.

M. Tao. (1970). Minimisation and Parameter Estimation in Image Restoration Variational Models with ℓ1-Constraints. East Asian Journal on Applied Mathematics. 8 (1). 44-69. doi:10.4208/eajam.210117.060817a
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