Diffusion Interpretation of Nonlocal Neighborhood Filters for Signal Denoising

Nonlocal neighborhood filters are modern and powerful techniques for image and signal denoising. In this paper, we give a probabilistic interpretation and analysis of the method viewed as a random walk on the patch space. We show that the method is intimately connected to the characteristics of diffusion processes, their escape times over potential barriers, and their spectral decomposition. In particular, the eigenstructure of the diffusion operator leads to novel insights on the performance and limitations of the denoising method, as well as a proposal for an improved filtering algorithm.