Denoising color images by reduced quaternion matrix singular value decomposition

Abstract

We propose a color-image-denoising algorithm that is based on the reduced quaternion matrix (RQM) of singular value decomposition (SVD). The new algorithm represents a color image as an RQM and handles such an image in a holistic manner. This algorithm can combine similar blocks from a noisy image by using a similar criterion. The proposed framework computes the optimal unitary matrix pair by using RQMSVD, and the coefficients of RQMSVD are obtained by projecting each block onto unitary matrices. The final filtered image is then obtained by manipulating the coefficients with hard threshold. The performance of the proposed algorithm is experimentally verified by using a variety of images and noise levels. Results demonstrate that the proposed algorithm is at par with or exceeds current state-of-the-art algorithms in both visual and quantitative performance.