PatchLift: Fast and Exact Computation of Patch Distances using Lifting, with Applications to Non-Local Means

In this paper, we propose a fast algorithm called PatchLift for computing distances between patches extracted from a one-dimensional signal. PatchLift is based on the observation that the patch distances can be expressed in terms of simple moving sums of an image, which is derived from the one-dimensional signal via lifting. We apply PatchLift to develop a separable extension of the classical Non-Local Means (NLM) algorithm which is at least 100× faster than NLM for standard parameter settings. The PSNR obtained using the proposed extension is typically close to (and often larger than) the PSNRs obtained using the original NLM. We provide some simulations results to demonstrate the acceleration achieved using separability and PatchLift.