Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries

TLDR

Image denoising aims to remove zero‑mean white Gaussian noise from images. The method learns a sparse, redundant dictionary with K‑SVD, trains it on either the corrupted image or a high‑quality database, and extends K‑SVD to arbitrary image sizes by imposing a global sparsity prior over all patches. The resulting Bayesian denoiser achieves state‑of‑the‑art performance, matching or surpassing recent leading methods.

Abstract

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.