Learning nonlinear spectral filters for color image reconstruction

This paper presents the idea of learning optimal filters for color image reconstruction based on a novel concept of nonlinear spectral image decompositions recently proposed by Guy Gilboa. We use a multiscale image decomposition approach based on total variation regularization and Bregman iterations to represent the input data as the sum of image layers containing features at different scales. Filtered images can be obtained by weighted linear combinations of the different frequency layers. We introduce the idea of learning optimal filters for the task of image denoising, and propose the idea of mixing high frequency components of different color channels. Our numerical experiments demonstrate that learning the optimal weights can significantly improve the results in comparison to the standard variational approach, and achieves state-of-the-art image denoising results.