多层次模极大值降噪算法研究

摘要

Wavelet modulus maximum denoising method has a superior property; while, the denoising performance is influenced by many factors when applied it in realistic environment, such as the optimal decomposition scale selection, shrinkage threshold estimate, modulus maximum line search and the efficiency and precision of reconstruction algorithm. On the basis of classic Mallat modulus maxima denoising algorithm the multilayer modulus maximum noise reduction algorithm is derived, in which the single select of the optimal decomposition scale is replaced by a range select. Also, the modulus maximum series are preprocessed by the improved threshold estimation, then the modulus maximum series are fast reconstructed by the polynomial interpolation. Finally the numerical results are presented by Matlab simulation strategy, and the result shows that multilayer modulus maximum noise reduction algorithm has a superior denoising performance and effectively resolves problems of the modulus maximum denoising faced in practical application.%小波模极大值去噪方法具有很好的理论基础,却在应用上存在许多影响去噪性能的因素,如最优分解尺度选择、收缩阈值估计、模极大值线搜索及重构算法的效率和精度。在经典Mallat模极大值去噪算法的基础上,提出多层次模极大值降噪算法,设定分解尺度的最优选择范围,并利用改进的自适应阈值估计对模极大值序列进行预处理及利用多项式插值对模极大值序列进行快速重构。Maltab仿真结果表明多层次模极大值降噪算法具有良好的去噪性能,有效解决模极大值去噪方法在实际应用中面临的问题。