Patch-based methods such as Non-Local Means (NLM) and BM3D have become the de facto gold standard for image denoising. The core of these approaches is to use similar patches within the image as cues for denoising. The operation usually requires expensive pair-wise patch comparisons. In this paper, we present a novel fast patch-based denoising technique based on Patch Geodesic Paths (PatchGP). PatchGPs treat image patches as nodes and patch differences as edge weights for computing the shortest (geodesic) paths. The path lengths can then be used as weights of the smoothing/denoising kernel.
We first show that, for natural images, PatchGPs can be effectively approximated by minimum hop paths (MHPs) that generally correspond to Euclidean line paths connecting two patch nodes. To construct the denoising kernel, we further discretize the MHP search directions and use only patches along the search directions. Along each MHP, we apply a weight propagation scheme to robustly and efficiently compute the path distance. To handle noise at multiple scales, we conduct wavelet image decomposition and apply PatchGP scheme at each scale. Comprehensive experiments show that our approach achieves comparable quality as the state-of-the-art methods such as NLM and BM3D but is a few orders of magnitude faster.