基于二维正交小波滤波器设计方法

A Convex Optimization Based Method to Design Two Dimensional Orthogonal Wavelet Filter Banks

为研究滤波器优化问题,针对传统的可分二维滤波器无法做到信号的独特频率响应特征,在正交二维不可分滤波器组的设计中幅频特性的非连续性问题,提出了一种基于凸优化理论的二通道二维不可分的正交小波滤波器组设计方法。首先利用多相位矩阵的范数来近似二维滤波器组重建条件以获得一个凸优化问题,然后利用内点法计算该凸优化问题全局最优解,把最优解作为第二步非线性优化过程的初始值,最后利用标准的非线性迭代算法计算原问题的最优解。在Matlab环境下进行了仿真实验,仿真结果表明,相对于传统的二维通滤波器,方法改进的最优滤波器保证原问题的最优解的同时具有更好的频率响应特征,解决了传统二维通滤波器存在的幅频特性非连续性问题,并供了一种可供选择的正交变换工具。

The traditional dividable two-dimensional filters do not have the unique signal frequency response characteristics. This paper presents a new theory based on convex optimization inseparable two-dimensional two-channel orthogonal wavelet filter design methods. The method uses multi-phase matrix to approximate the norm of two-dimensional reconstruction filter conditions to obtain a convex optimization problem,and then calculate the convex optimization problem using interior point method with the global optimal solution as the initial value in the second step of the non-linear optimization process. Using a standard non-linear iterative algorithm to obtain the original optimal solution. Simulation results show that the optimum obtained by the filter has good frequency response characteristics and optimal solution of the.original problem