Adaptive Parameter Selection for Gradient-Sparse Plus Low Patch-Rank Recovery: Application to Image Decomposition

In this work, we are interested in gradient sparse plus low patch-rank signal recovery for image structure-texture decomposition, the structure being gradient-sparse and the texture low patch-rank. Based upon theoretical results of sparse plus low-rank matrix recovery, we propose an algorithm to automatically tune the regularization parameters of our model depending on the content of the image. This permits to provide an improved localized version of gradient sparse plus low patch- rank decomposition. This algorithm is validated by experiments on synthetic and real images.