Image denoising: Learning the noise model via nonsmooth PDE-constrained optimization

Abstract

We propose a nonsmooth PDE-constrained optimization approach for the determination of the correctnoise model in total variation (TV) image denoising. Anoptimization problem for the determination of the weightscorresponding to different types of noise distributions is stated and existence of an optimal solution isproved. A tailored regularization approach for the approximation of the optimalparameter values is proposed thereafter and its consistencystudied. Additionally, the differentiability of the solution operatoris proved and an optimality system characterizing the optimalsolutions of each regularized problem is derived. The optimal parameter values are numerically computed by using aquasi-Newton method, together with semismooth Newton type algorithms for the solution of the TV-subproblems.