Fast Separable Non-Local Means

TL;DR

This paper introduces PatchLift, a fast algorithm for computing patch distances in one-dimensional signals, enabling a separable Non-Local Means denoising method that is faster and often more effective than traditional approaches.

Contribution

The paper presents PatchLift, a novel efficient technique for patch distance computation that significantly accelerates separable NLM denoising while improving quality.

Findings

PatchLift computes patch distances independently of patch length.

Separable NLM with PatchLift is several times faster than standard NLM.

The proposed method outperforms traditional NLM in PSNR, SSIM, and visual quality.

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.