Image denoising via bidirectional low rank representation with cluster adaptive dictionary

Abstract

In this study, the authors propose a new image representation model that fully exploits the similarity inherent in natural images. The idea is based on an observation of similar patches. For a clean image, when a cluster of similar patches are collected to form the similar patch matrix (SPM), there exists high correlation among columns/rows of the SPM. This implies that, when the column/row vectors are linearly expressed by a dictionary, their coefficients of columns/rows should have high correlation, which leads to the coefficient matrixes of column/row representation are low-ranked. This observation inspires them to propose a novel image denoising model named bidirectional low rank representation (BiLRR) with cluster adaptive dictionary. Specifically, they use low rank penalties simultaneously on the coefficient matrixes of column and row representations to recover the correlation structure of the SPM. Meanwhile, a cluster adaptive dictionary is learned to represent each SPM so as to well preserve the fine structure of image. By applying variable splitting and penalty technique, they present an efficient alternative minimisation algorithm to solve the proposed BiLRR model. Experimental results indicate the authors’ method achieves a competitive denoising performance in comparison with state-of-the-art algorithms in terms of subjective and objective qualities.