Monte-Carlo SURE: A Black-Box Optimization of Regularization Parameters for General Denoising Algorithms - Supplementary Material

This material supplements some sections of the paper entitled “Monte-Carlo SURE: A Black-Box Optimization of Regularization Parameters for General Denoising Algorithms”. Here, we elaborate on the solution to the differentiability issue associated with the Monte-Carlo divergence estimation proposed (in Theorem 2) in the paper. Firstly, we verify the validity of the Taylor expansion-based argumentation of Theorem 2 for algorithms like total-variation denoising (TVD). Following that, we give a proof of the second part of Theorem 2 which deals with a weaker hypothesis (using tempered distributions) of the problem.