Non-local patch regression: Robust image denoising in patch space

It was recently demonstrated in [13] that the denoising performance of Non-Local Means (NLM) can be improved at large noise levels by replacing the mean by the robust Euclidean median. Numerical experiments on synthetic and natural images showed that the latter consistently performed better than NLM beyond a certain noise level, and significantly so for images with sharp edges. The Euclidean mean and median can be put into a common regression (on the patch space) framework, in which the ℓ² norm of the residuals is considered in the former, while the ℓ¹ norm is considered in the latter. The natural question then is what happens if we consider ℓ^p (0 <; p <; 1) regression? We investigate this possibility in this paper.