A Class of Multi-scale Models for Image Denoising in Negative Hilbert-Sobolev Spaces

Abstract

In this paper, we propose a class of multi-scale variational models for image denoising. Our models decompose a given image into two parts: geometric component representing the objects in the image and oscillatory component representing the noise or texture. Considering different components belong to different scale spaces and oscillatory components have small norm in negative Sobolev spaces, we propose multi-scale models image denoising in negative Sobolev space. Numerical results show that our models are flexible and efficient for preserving texture when denoising image.