Singular value decomposition of split quaternion matrices and its applications for color image processing

As there is a strong spectral link among the three color channels of a color image, a color image model based on four-dimensional algebra ensures an intrinsic link among the channels and creates an approach for color image compression. We propose a theory of singular value decomposition of split quaternion matrices using a special 2×2 real representation matrix structure and provide an effective and efficient algorithm to deal with the color image compression problem. Numerical examples show that under the same compression conditions, the proposed algorithm outperforms the quaternion color image compression method and traditional three-color channel compression method in terms of fidelity, measured by peak signal-to-noise ratio and structural similarity. It has been proven to be a highly competitive method, with a balance of efficiency and performance that makes it a standout choice.