Image denoising in the presence of non-Gaussian, power-law noise

In image processing, noise is usually modeled as white Gaussian noise to represent general sensor and environmental clutter, and many effective methods have been developed to remove Gaussian noise. We show here that in many situations, such as Terahertz (ThZ) images or under-water images distorted by wavy surface, noise may be highly non-Gaussian, and even heavy-tailed with power-law distributions. We perceive that such noise may be ubiquitous, such as in images obtained by radar, LIDAR, satellite, and electro-optical visual cameras, in unsteady environments. We show that such noise cannot be effectively reduced by even the best method (block-matching 3D transformation, BM3D) for removing Gaussian noise. A fundamental issue arises of how to develop a proper framework to aptly deal with such non-Gaussian noise. We propose a viable new approach using power-law analysis, and evaluate its effectiveness using well-known images in computer vision community. We show that the new approach, which we call thresholding-median filtering and BM3D (TM-BM3D), works effective on all known types of noise, Gaussian, salt and pepper, and power-law noise.