Image denoising via correlation-based sparse representation

Abstract

Error-based Orthogonal Matching Pursuit employed in many image denoising algorithms (e.g., K-means singular value decomposition (K-SVD) algorithm) tries to reconstruct the clean image patch by projecting the observed noisy patch onto a dictionary and picking the atom with maximum orthogonal projection. This approach does indeed minimize the power in the residual. However, minimizing the power in the residual does not guarantee that selected atoms will match the clean image patch. This leaves behind a residual that contains structures from the clean image patch. This problem becomes more pronounced at high noise levels. We propose a simple correlation-based sparse coding algorithm that is better able to pick the atom that matches the clean patch. This is achieved by picking atoms that force the residual patch to have autocorrelation similar to the autocorrelation of contaminating noise. Autocorrelation-based sparse coding and dictionary update stages are iterated, and dictionaries are learned from noisy image patches. The proposed algorithm is compared with the K-SVD denoising algorithm, BM3D and EPLL algorithms. Our results indicate that the proposed algorithm is significantly better than K-SVD and EPLL denoising. At the noise power 100, the improvement over K-SVD denoising algorithm for Barbara and fingerprint images is 1.14 and 2.64 dB, respectively. The proposed algorithm gives results that are visually comparable or better than BM3D algorithm.