Abstract

A key issue in image denoising is an adequate choice of the correct noise model. In a variational approach this amounts to the choice of the data fidelity and its weighting. Depending on this choice, different results are obtained. In this talk I will discuss a PDE -constrained optimization approach for the determination of the noise distribution in total variation (TV) image denoising. An optimization problem for the determination of the weights correspondent to different types of noise distributions is stated and existence of an optimal solution is proved. A tailored regularization approach for the approximation of the optimal parameter values is proposed thereafter and its consistency studied. Additionally, the differentiability of the solution operator is proved and an optimality system characterizing the optimal solutions of each regularized problem is derived. The optimal parameter values are numerically computed by using a quasi-Newton method, together with semismooth Newton type algorithms for the solution of the TV-subproblems. The talk is furnished with numerical examples computed on simulated data.

This is joint work with Juan Carlos De Los Reyes