基于Hermite插值的小波变换模极大值重构信号快速算法

Fast Reconstruction Algorithm Based on Hermite Interpolation from Modulus Maxima of Wavelet Transform

信号在不同尺度上的小波变换模极大值包含了信号中的重要信息,因此研究如何由小波变换模极大值重构信号是很有意义的。论文提出了一种基于Hermite插值多项式由二进小波变换模极大值重构信号的快速算法。数值试验表明,与S.Mallat提出的经典交替投影算法相比,该算法可以在保证重构质量的前提下简化计算过程,提高计算效率,计算所需时间与交替投影算法相比大大减少,是一种实用性较强的信号重构算法。

The modulus maxima of a signal＇s wavelet transform on different levels contain me most important mtormauon of the signal, so it is a meaningful work to find out how to reconstruct wavelet coefficients form the modulus maxima. A fast algorithm based on Hermite interpolation polynomial for reconstructing signal from its wavelet transform maxima was proposed. Numerical experiments show that compared with the classical alternating projection algorithm proposed by S.Mallat, this algorithm is simpler, more efficient, and it can keep high reconstruction signal to noise ratio at the same time. The computing time of this algorithm is more less compared with that of S,Mallat＇s, so it is a practical fast reconstruction algorithm.