基于四元数矩阵奇异值分解的彩色图像分解

摘要

讨论了四元数矩阵的奇异值分解(QSVD),四元数矩阵的奇异值仍是正实数,但两个酉矩阵是含有四元数的四元数矩阵.给出通过四元数矩阵的等价实矩阵求解QSVD的有效算法.最后应用QSVD进行彩色图像分解,并给出了在Fruits、Baboon等图像上的实验结果.QSVD使许多基于SVD的图像处理方法可以推广到彩色图像处理上而不用再将彩色图像分解成三个通道图像进行处理.%The singular value decomposition of a quatemion matrix (QSVD) is discussed.The singular values of a quatemion matrix are still real and positive, but the two unitary matrices　　are quaternion matrices with quatemion 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.