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

The modulus maxima of a signal’s wavelet transform on different levels contain the most important information 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.