(untitled) (Journal of Computational Mathematics, 2021)
This article introduces a novel variational model for restoring images degraded by Cauchy noise and/or blurring. The model integrates a nonconvex data-fidelity term with two regularization terms, a sparse representation prior over dictionary learning and total generalized variation (TGV) regularization. The sparse representation prior exploiting patch information enables the preservation of fine features and textural patterns, while adequately denoising in homogeneous regions and contributing natural visual quality. TGV regularization further assists in effectively denoising in smooth regions while retaining edges. By adopting the penalty method and an alternating minimization approach, we present an efficient iterative algorithm to solve the proposed model. Numerical results establish the superiority of the proposed model over other existing models in regard to visual quality and certain image quality assessments.