Adaptive Graph Filtering with Intra-Patch Pixel Smoothing for Image Denoising

Abstract

Graph filtering has recently attracted significant attention in signal processing. This study proposes an adaptive graph filtering method with intra-patch pixel smoothing (AWGF-PS) to improve the quality of denoised images. A detailed coefficient shrinkage algorithm is provided for the graph filter, which makes the noisy component in each graph frequency band adaptively shrink with its component significance. It replaces the traditional ideal low-pass graph filter and is better at removing image noise in the entire band. As for the design of the graph filters whose performance depends heavily on the topological structure among signals, we infer the graph from the super-pixels of similar patches by considering the smoothing attribute of intra-patch pixels. This graph fully exploits the relationship among the pixels in local areas. Moreover, it can achieve an efficient calculation of graph Fourier bases on a small-scale graph, which effectively enhances the graph filtering’s practicality. The experiments demonstrate that our AWGF-PS method suitably restores the denoised images. It outperforms several state-of-the-art model-based methods and is competitive with certain discriminative learning methods. In particular, it has more advantages in tackling images with significant noise.