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.

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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.

  • History

Published online: 2018-02

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