基于提升算法的自适应小波变换及应用

为了克服传统小波变换的不足，提出了一种用样本相关性检测信号特征的自适应小波变换降噪方法。该方法以第二代小波变换为基础，用变换样本与相邻样本之间的相关性，来检测信号的局部特征。并根据相关系数的大小，来确定每一尺度上的每个样本的最佳预测器和更新器，使小波能够较好地适应信号的局部特征。在信号相关性强的情况下，采用了最优插值估计的改进算法。模拟实验和工程应用的结果表明，该方法克服了传统小波变换降噪方法丢失原始信号局部信息的缺陷，不仅可以有效地去除原始信号中的噪声，而且能够保留原始信号的局部特征。

Self-adoptive wavelet transformation based on ascending algorithm and its application

For the sake of overcoming the insufficiency of the traditional wavelet transformation, a kind of self-adopting wavelet transformation noise reduction method using the sample interrelation to detect the signal features had been put forward. This method takes the second generation wavelet transformation as a base, using the interrelation between transformation sample and adjacent sample to detect partial feature of the signal, and according to the magnitude of related coefficient to define the optimal pre-detector and re-newer of every sample in every dimension, so as to let the wavelet be able to suit fairly the partial feature of the signal. The improved algorithm of optimal interpolative estimation was adopted under the condition of strong signal interrelation. The results of simulation experiment and engineering application showed that this method overcame the deficiency of the traditional wavelet transformation noise reduction method would lose partial information of the primary signal, thus it could not only effectively eliminate the noise in the primary signal but also could retain partial features of the primary signal.