Artifact reduction for separable nonlocal means

It was recently demonstrated [J. Electron. Imaging, 25(2), 2016] that one can perform fast non-local means (NLM) denoising of one-dimensional signals using a method called lifting. The cost of lifting is independent of the patch length, which dramatically reduces the run-time for large patches. Unfortunately, it is difficult to directly extend lifting for non-local means denoising of images. To bypass this, the authors proposed a separable approximation in which the image rows and columns are filtered using lifting. The overall algorithm is significantly faster than NLM, and the results are comparable in terms of PSNR. However, the separable processing often produces vertical and horizontal stripes in the image. This problem was previously addressed by using a bilateral filter-based post-smoothing, which was effective in removing some of the stripes. In this letter, we demonstrate that 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 NLM), while still using one-dimensional patches (as in the previous proposal). The novelty is in the observation that one can use lifting for performing two-dimensional searches. The proposed approach produces artifact-free images, whose quality and PSNR are comparable to NLM, while being significantly faster.