Combined non-local and multi-resolution sparsity prior in image restoration

In the field of image denoising, the non-local means (NLMS) filter is a conceptually simple, yet powerful technique. This filter exploits non-local, i.e. spatially repetitive, structure in natural images to estimate noise-free structure. In contrast, a wide variety of image restoration problems have been solved exploiting local smoothness of natural images, e.g. by enforcing sparsity of images when subjected to a multi-resolution transform. In this paper we introduce the prior knowledge of non-local repetitiveness of image structures into a broad multi-resolution image restoration framework. The proposed framework allows the power of the NLMS filter, supplemented by multi-resolution sparsity, to be extended for a wide variety of image restoration problems, such as demosaicing, deconvolution, reconstruction from insufficient measurements,... in a conceptually simple way.