Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries

We address the image denoising problem, where zero-mean white and homogeneous Gaussian additive noise is to be removed from a given image. The approach taken is based on sparse and redundant representations over trained dictionaries. Using the K-SVD algorithm, we obtain a dictionary that describes the image content effectively. Two training options are considered: using the corrupted image itself, or training on a corpus of high-quality image database. Since the K-SVD is limited in handling small image patches, we extend its deployment to arbitrary image sizes by defining a global image prior that forces sparsity over patches in every location in the image. We show how such Bayesian treatment leads to a simple and effective denoising algorithm. This leads to a state-of-the-art denoising performance, equivalent and sometimes surpassing recently published leading alternative denoising methods

I. Introduction

In this paper, we address the classic image denoising problem: An ideal image is measured in the presence of an additive zero-mean white and homogeneous Gaussian noise, , with standard deviation . The measured image is, thus $${\bf y}={\bf x}+{\bf v}. \eqno{\hbox{(1)}}$$ We desire to design an algorithm that can remove the noise from , getting as close as possible to the original image, .