小波变换的稀疏最优化信号趋势项提取方法

Sparse optimization methods for signal trend term extraction based on wavelet transform

针对非线性信号的趋势项,提出一种基于小波变换的稀疏最优化方法(WT-SO)。该方法通过设置两个边界约束条件,求取l1范数稀疏最优解重构信号趋势项。仿真信号与实测信号处理结果表明:该方法依据信号自身的特性来定义趋势项,不需要对信号作任何假设,比传统的提取趋势项的方法具有更高的精度和可靠性,且在各种噪声环境下均具有良好的鲁棒性。

In view of the trend term of nonlinear signal, propose a sparse optimization method based on wavelet transform. The method calculates the l1 norm sparse optimal solution to reconstruct the trend of signal by setting two boundary constraints. Simulation signal and measured signal processing result show that the method define trend item according to its self characteristic, don＇ t need to make any assumptions and it is fully data-driven, and has a good robustness in different noise intensity environment,the method has higher precision and reliability than the traditional method.