一种改进雅可比算法的频域临界采样图滤波器组

A critically sampled graph filter banks with spectral domain sampling based on improved Jacobi algorithm

频域临界采样图滤波器组需要对拉普拉斯矩阵进行特征分解,这导致了该框架计算复杂度过高。针对该问题,采用改进雅可比算法近似求解该框架的特征矩阵,从而降低计算复杂度。改进的雅可比算法将近似求解特征矩阵的问题归结为一个带约束的优化问题,将拉普拉斯矩阵的近似误差作为目标函数,以近似特征矩阵的稀疏正交性作为约束条件,从而求解出近似特征矩阵。理论和仿真实验结果表明,近似特征矩阵用于频域临界采样图滤波器组不会改变其完全重构条件,且与现有的频域临界采样图滤波组相比,改进的雅可比算法在降低计算复杂度的同时保持了良好的去噪性能。

Critically sampled graph filter banks with spectral domain sampling requires to perform eigendecomposition of the Laplacian matrix,which leads to high computational complexity.To solve this problem,an improved Jacobi algorithm is proposed to approximate the eigenmatrix of the framework to reduce the computational complexity.In this algorithm,the approximate solution of eigenmatrix is formulated into a constrained optimization problem,whose objective function is the approximation error of Laplacian matrix,and the constraint function is the sparse orthogonality of the approximate eigenmatrix.Theoretical and simulation experiments show that using the approximate feature matrix in the filter banks will not destroy its perfect reconstruction conditions.Compared with the existing critically sampled graph filter banks with spectral domain sampling,the improved algorithm reduces the computational complexity while maintaining good denoise performance.