Image Restoration under Cauchy Noise with Sparse Representation Prior and Total Generalized Variation (Journal of Computational Mathematics, 2021)
This article introduces a novel variational model for restoring images degraded byCauchy noise and/or blurring. The model integrates a nonconvex data-fidelity term withtwo regularization terms, a sparse representation prior over dictionary learning and totalgeneralized variation (TGV) regularization. The sparse representation prior exploitingpatch information enables the preservation of fine features and textural patterns, whileadequately denoising in homogeneous regions and contributing natural visual quality. TGVregularization further assists in effectively denoising in smooth regions while retainingedges. By adopting the penalty method and an alternating minimization approach, wepresent an efficient iterative algorithm to solve the proposed model. Numerical resultsestablish the superiority of the proposed model over other existing models in regard tovisual quality and certain image quality assessments.
Keywords: Image restoration; Cauchy noise; Sparse representation prior; Dictionary learning; Total generalized variation.