Image Restoration Using Variational Approaches: Some Recent Advances

In image formation, the observed images are usually blurred by optical instruments and/or transfer medium and contaminated by noise, which makes image restoration a classical inverse problem. A general principle for dealing with the intrinsic numerical instability of most inverse problems is that of regularization. Among the regularization approaches the most common is Tikhonov regularization. Another very popular choice in the literature for regularization is based on the Total Variation (TV) norm. Since then, in order to provide more reliable and efficient models, several variational formulations have been investigated which involve two terms, the data-fidelity term and the regularization term, with the goal to capture characteristic and essential image features. In this review, we will focus on variational methods for the restoration of images corrupted by additive noise which we assume to be sampled from a known a-priori distribution. In particular, we will discuss recent advanced proposals for the regularization and fidelity terms in the optimization problem. Numerical results illustrate the efficacy of the different models.