基于小波域维纳滤波器的信号稀疏表示

Sparse Representation of Signals Based on Wavelet Domain Wiener Filtering

经典小波分解对信号稀疏化效果不佳,为此设计了基于小波域经验维纳滤波器的稀疏表示算法.该算法可自适应地衰减每个小波系数,增大系数的稀疏度及可压缩性,从而提高压缩感知算法对信号的恢复质量.仿真结果表明,与传统的基于小波变换的信号稀疏表示及恢复算法相比,该算法较大地提升了对信号及图像的恢复质量.

A wavelet-based Wiener filter is proposed for signal sparse representation since the classical wavelet transform can not posses good sparse results for real signals. The proposed method can adaptively decrease the magnitude of each wavelet coefficient so that sparsity and compressibility of the wavelet coefficients is improved. This results in improvement of recovered signal quality of the compressed sensing algorithm. Simulation results show that, compared to the original sparse representation based on wavelet transform, the proposed algorithm can significantly improve quality of recovered signals for both signals and images.