Li Ying, Wei Musheng, Zhang Fengxia, Zhao Jianli
College of Mathematical Sciences, Liaocheng University, Shandong, P. R. China.
College of Mathematics and Science, Shanghai Normal University, Shanghai, P. R. China.
PLoS One. 2017 Mar 3;12(3):e0172746. doi: 10.1371/journal.pone.0172746. eCollection 2017.
Color image compression is a commonly used process to represent image data as few bits as possible, which removes redundancy in the data while maintaining an appropriate level of quality for the user. Color image compression algorithms based on quaternion are very common in recent years. In this paper, we propose a color image compression scheme, based on the real SVD, named real compression scheme. First, we form a new real rectangular matrix C according to the red, green and blue components of the original color image and perform the real SVD for C. Then we select several largest singular values and the corresponding vectors in the left and right unitary matrices to compress the color image. We compare the real compression scheme with quaternion compression scheme by performing quaternion SVD using the real structure-preserving algorithm. We compare the two schemes in terms of operation amount, assignment number, operation speed, PSNR and CR. The experimental results show that with the same numbers of selected singular values, the real compression scheme offers higher CR, much less operation time, but a little bit smaller PSNR than the quaternion compression scheme. When these two schemes have the same CR, the real compression scheme shows more prominent advantages both on the operation time and PSNR.
彩色图像压缩是一种常用的过程，旨在用尽可能少的比特来表示图像数据，该过程在去除数据冗余的同时，为用户保持适当的质量水平。近年来，基于四元数的彩色图像压缩算法非常普遍。在本文中，我们提出了一种基于实奇异值分解（real SVD）的彩色图像压缩方案，称为实压缩方案。首先，根据原始彩色图像的红、绿、蓝分量形成一个新的实矩形矩阵C，并对C进行实奇异值分解。然后，我们在左右酉矩阵中选择几个最大奇异值和相应的向量来压缩彩色图像。我们使用实结构保持算法通过执行四元数奇异值分解，将实压缩方案与四元数压缩方案进行比较。我们从运算量、赋值次数、运算速度、峰值信噪比（PSNR）和压缩率（CR）方面对这两种方案进行比较。实验结果表明，在选择相同数量奇异值的情况下，实压缩方案具有更高的压缩率、更少的运算时间，但峰值信噪比比四元数压缩方案略小。当这两种方案具有相同的压缩率时，实压缩方案在运算时间和峰值信噪比方面都表现出更突出的优势。
