Fast separable nonlocal means

Abstract

We propose a simple and fast algorithm called PatchLift for computing distances between patches (contiguous block of samples) extracted from a given one-dimensional signal. PatchLift is based on the observation that the patch distances can be efficiently computed from a matrix that is derived from the one-dimensional signal using lifting; importantly, the number of operations required to compute the patch distances using this approach does not scale with the patch length. We next demonstrate how PatchLift can be used for patch-based denoising of images corrupted with Gaussian noise. In particular, we propose a separable formulation of the classical Non-Local Means (NLM) algorithm that can be implemented using PatchLift. We demonstrate that the PatchLift-based implementation of separable NLM is few orders faster than standard NLM, and is competitive with existing fast implementations of NLM. Moreover, its denoising performance is shown to be consistently superior to that of NLM and some of its variants, both in terms of PSNR/SSIM and visual quality.

Artifact reduction for separable nonlocal means

“…We proposed a method that uses the idea of lifting from previous work 13 to perform fast non-local means denoising of images. The proposed method does not give rise to undesirable artifacts (as was the case with the original proposal), and produces images whose denoising quality and PSNR/SSIM are comparable to non-local means.…”

“…We see that F is the smoothed version of F, obtained by box filtering F along its sub-diagonals. The important observation 13 is that we can write…”

“…The present focus is on a recent separable approximation of NLM. 13 At the core of this proposal is a method called lifting, which computes the NLM of a one-dimensional signal using O(S) operations per sample. In other words, the complexity of lifting is independent of the patch length K. Extending lifting for NLM denoising of images, however, turns out to be a difficult task.…”

“…In other words, the complexity of lifting is independent of the patch length K. Extending lifting for NLM denoising of images, however, turns out to be a difficult task. Therefore, we proposed a separable approximation, called separable NLM (SNLM), 13 in which the rows and columns of the image are independently filtered using lifting. In particular, we separately computed the "rows-then-columns" and "columns-then-rows" filtering, which were then optimally combined.…”

“…In this work, we demonstrate that the stripes can be mitigated in the first place simply by involving the neighboring rows (or columns) in the filtering. In other words, we use a two-dimensional search (similar to classical NLM 1 ), while still using one-dimensional patches (as done previously 13 ). The present novelty is in the observation that one can use lifting for performing a two-dimensional search.…”