A fast signal reconstruction algorithm from wavelet transform modulus maxima

Based on the wavelet multiscale analysis theory, a fast signal reconstruction algorithm from its wavelet transform modulus maxima(WTMM) is presented here. The WT coefficients in each scale are reconstructed by using monotone piecewise cubic Hermite interpolation polynomial between two modulus maxima points. If the signs of two neighborhood modulus maxima are the same, we add a new interpolation point between them. This method has explicit physical meaning. It is less complex and can be implemented conveniently. Numerical results show that the proposed reconstruction approach is effective and to a better solution than the algorithm in [1] and [5].