重构小波系数的分段三次样条播值新算法

利用小波变换模极大值原理对信号去噪之后，如何由保留下来的模极大值点恢复出满意的重构信号，是一个重要课题。本文首先分析模极大值与小波系数之间的内在关系，提出了模极大值实际上是小波系数在特定意义下的离散采样；然后给出了一种对模极大值进行预处理的方法，由此得到了一组新的伪模极大值序列；利用这组伪模极大值序列，提出了一种新的重构小波系数的分段三次样条播值（ＰＣＳＩ）新算法，该算法程序简单，易实现，克服了交替投影（ＡＰ）法计算量大、程序复杂等缺点；最后给出一个应用实例，实验结果表明，与经典的交替投影法相比，本文提出的ＰＣＳＩ算法可获得更高的重构信号信噪比增益和更小的相对均方误差，它是一种实际、有效的算法。

A New Piecewise Cubic Spline Interpolating Algorithm for the Reconstruction of Wavelet Coefficients

When a denoised process is performed on a signal with wavelet transform modulus maximum principle, how to reconstruct a satisfactory signal from remained modulus maxhoa is an important subject. In this paper, an analysis is made on the relationship between the modulus maxima ed wavelet coefficientS. Then the fat that modulus maxboa are anally discrete samples of wavelet coefficient in a specific sense is obtained. By preprocessing the modulus maxima we get a new sat of pseudo modulus maximum sequence with Which a new piecewise cubic spline interpolating (PCSI) algorithm to reconstruct the wavelet coefficients is presented. Compared. with the alternate projection (AP) method, this algorithm is simple and easy to implement. Finally, an example is given and the experimental results show that PCSI algorithm can get higher reconstruotion signal SNR gain and small.er RMSE than alternate projection method, so it is a practical and efficient algorithm.