Proximity algorithms for the L1/TV image denoising model
The authors introduce a proximity operator framework for the direct treatment of the L1/TV image denoising model. The L1/TV image denoising model minimizes the sum of a data fidelity term measured in the \(\ell^1\)-norm and the total-variation regularization term. In this paper, a general model constructed as a minimization of the sum of the \(\ell^1\) fidelity term, an indicator term and a regularization term in the form of the composition of a convex function and a matrix is investigated. The difficulties in the numerical treatment of this model caused by its nondifferentiability are overcome by introducing a new fixed-point equation. An alternative model replacing the nondifferentiable convex function in the formulation of the total variation with its differentiable Moreau envelope is presented, too. Numerical results are presented for impulsive noise removal to demonstrate the approximation accuracy and computational efficiency of the proposed algorithm. The obtained results can be widely used, e.g. in computer vision, biomedical imaging, optical flow, object tracking and shape denoising.
scientific article; zbMATH DE number 6153898
scientific article