Texture Preserving Variational Denoising Using an Adaptive Fidelity Term

Denoising algorithms based on gradient dependent energy functionals, such as Perona-Malik and total variation denoising, modify images towards piecewise constant functions. Although edge sharpness and location is well preserved, important information, encoded in image features like textures or certain details, is often compromised in the process of denoising. We propose a mechanism that better preserves fine scale features in such denoising processes. This is accomplished by adding a spatially varying fidelity term that locally controls the extent of denoising over image regions according to their content. Local variance measures of the oscillatory part of the signal are used to compute the adaptive fidelity term. Our results show improvement in the signal-tonoise ratio over scalar fidelity term processes, and they are more appealing visually. This type of processing is relatively simple, can be used for a variety of tasks in PDE-based image processing and computer vision, and is stable and meaningful from a mathematical viewpoint.