A principled approach to image denoising with similarity kernels involving patches

Denoising is a cornerstone of image analysis and remains a very active research field. This paper deals with image filters that rely on similarity kernels to compute weighted pixel averages. Whereas similarities have been based on the comparison of isolated pixel values until recently, modern filters extend the paradigm to groups of pixels called patches. Significant quality improvements result from the mere replacement of pixel differences with patch-to-patch comparisons directly into the filter. Our objective is to cast this generalization within the framework of mode estimation. Starting from objective functions that are extended to patches, this leads us to slightly different formulations of filters proposed in the literature, such as the local M-smoothers, bilateral filters, and the nonlocal means. A fast implementation of these new filters relying on separable linear-time convolutions is detailed. Experiments show that this principled approach further improves the denoising quality without increasing the computational complexity.