Abstract: The singular value decomposition of a quaternion matrix (QSVD) is discussed. The singular values of a quaternion matrix are still real and positive, but the two unitary matrices are quaternion matrices with quaternion entries. An efficient algorithm to compute QSVD by the SVD of its equivalent real matrix is presented. Finally, QSVD is applied to color image decomposition, and the experimental results on the images Fruits and Baboon are shown. By using of QSVD, many image processing methods based on SVD can be extended for color image without separating it into three channel images.

Key words: the singular value decomposition of a quaternion matrix (QSVD), color image decomposition, peak signal-to-noise ratio (PSNR)