Abstract:

Images are inevitably corrupted by noise during transition and acquisition, which exerts a considerable influence on the subsequent processing. Therefore, image denoising is essential for image processing. Specially, the critical challenge of image denoising is to remove the noise while preserving information as much as possible. Generally, the group-based sparse representation model is exploited to restore the clean image, due to the self-similarity of natural images. This paper offered a novel color image denoising method that utilized quaternions in the group sparsity model, where each pixel was expressed as a pure quaternion. Initially, each pixel of the observed image was expressed as a quaternion unit, and a quaternion patch group matrix was established by Pearson′s correlation coefficient. The proposed model then learnt the dictionary for each patch group, working well with the pursuit algorithm. In other words, the group-based sparsity method assumed that each patch group was a linear combination of the basic elements of the dictionary. Unfortunately, it remained arduous to reconstruct the image structure precisely. Therefore, the group sparsity model incorporated kernel Wiener filtering to enhance image structure quality. In contrast to the traditional models, the new model not only worked with the corresponding RGB channels, but also leveraged the relationship between patches. Fueled by the exploration of the inner correlation of color channels, the proposed method could preserve the image information as much as possible while removing noise. The experiments validated the efficiency of the proposed method both in numerical results and visual performance on different noise levels.

Key words: image denoising, quaternion analysis, patch grouping, principal component analysis, sparse representation