小波系数阈值估计的改进模型

Better Threshold Estimation of Wavelet Coefficients for Improving Denoising

讨论了小波阈值去噪中估计小波系数的软阈值和硬阈值方法 ,然后针对硬阈值法不连续和软阈值法有偏差的缺点 ,提出了 3种改进方法 ,即多项式插值法 ,软、硬阈值折衷法和模平方处理方法 ,并给出这 3种估计器模型 ,它们都不同程度地克服了软阈值和硬阈值方法中固有的缺点。通过数值试验对这些方法进行比较 ,结果发现 ,这 3种改进的小波系数阈值估计模型用于信号去噪时 ,比单纯的软阈值和硬阈值方法均获得了更高的信噪比增益。

Existing models for threshold estimation of wavelet coefficients are not quite satisfactory for denoising. To avoid the discontinuity caused by using the hard-thresholding model and the biased estimation caused by using the soft-thresholding model, we present three improved models of threshold estimation. These three models are: polynomial interpolating model, compromise model (in between the hard-thresholding and soft-thresholding models), and the modulus squared model. For the first and third improved models, the wavelet coefficients estimated are continuous at the threshold; for these same two models, bias in estimated wavelet coefficients is much reduced and, for the first improved model, when the original coefficients are large, bias becomes almost negligible. The experimental results show preliminarily that all three improved models can give higher SNR (Signal to Noise Ratio) gain than obtainable with the soft-thresholding or hard-thresholding model.