Fast Edge-Aware Denoising by Approximated Patch Geodesic Paths

Patch-based denoising, while effective, requires expensive pairwise patch comparisons. We present a novel fast patch-based denoising technique based on patch geodesic paths (PatchGPs). PatchGPs treat image patches as nodes and patch differences as edge weights for computing the shortest (geodesic) paths. The distance defined by the PatchGP can then be used as a similarity metric for image denoising. We first show that, for natural images, PatchGPs can be approximated by minimum hop paths (MHPs) that correspond to Euclidean line paths connecting two patch nodes. The denoising kernel is constructed using patches along discretized MHP search directions. We apply a weight propagation scheme to robustly and efficiently compute the path distance for each MHP. Our technique handles noise at multiple scales by analyzing the noise distribution (through wavelet decomposition) at each scale. Experiments show that our approach maintains the high quality of patch-based denoising but is a few orders of magnitude faster. We also demonstrate how PatchGP can be used for fast Bayer pattern (raw) denoising and image detail enhancement.