PDE-based denoising of complex scenes using a spatially-varying fidelity term

The widely used denoising algorithms based on nonlinear diffusion, such as Perona-Malik and total variation denoising, modify images toward piecewise constant functions. Though edge sharpness and location is well preserved, important information, encoded in image features like textures or small details, is often lost in the process. We suggest a simple way to better preserve textures, small details, or global information. This is done by adding a spatially varying fidelity term that controls the amount of denoising in any region of the image. This form is very 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 point of view.