基于TSVD的高阶图像低秩近似新方法

A NEW LOW RANK APPROXIMATION METHOD FOR HIGH-ORDER IMAGE BASED ON TSVD

提出一种基于广义奇异值分解的高阶图像低秩近似新方法。在传统矩阵分析的基础上,介绍高阶广义矩阵的生成及定义,得出广义奇异值分解不仅适用于传统的实数矩阵,对高阶广义复数矩阵亦具有重要意义。实验在高阶图像低秩近似的基础上,提出两种改进方案,一是将传统的实数矩阵扩展成为高阶广义复数矩阵,二是在领域选取时,分析比较指数增长和线性增长方式的近似效果。数值实验验证了高阶广义复数矩阵具有更高的低秩近似效果,指数增长方式与线性增长方式相比具有明显的优越性。

This paper proposes a new low rank approximation method for high-order image based on TSVD.On the basis of traditional matrix analysis,the generation and definition of high-order generalized matrix were introduced.It was concluded that generalized singular value decomposition was not only suitable for traditional real matrix,but also important for high-order generalized complex matrix.Based on the low-rank approximation of high-order images,two improved schemes were proposed.One was to extend the traditional real matrix to the high-order generalized complex matrix.The other was to compare with the approximation effects of exponential growth and linear growth in the field selection.The numerical experiments show that the higher-order generalized complex matrix has a higher approximation effect of low rank,and the exponential growth mode is superior to the linear growth mode.