Signal reconstruction from the wavelet transform modulus maxima

We define all the a priori constraints available in the wavelet transform modulus maxima representation and describe an iterative scheme involving minimum distance, nonexpansive projections onto convex spaces for the reconstruction of signal from its wavelet transform modulus maxima. The scheme is able to exploit all the constraints available in the representation. The method of quadratic programming is used to implement the minimum distance projection that corresponds to the convex component of the modulus maxima constraint. Simulation results show that our reconstruction method always converges monotonically and to a better solution than the algorithms by S. Mallat and W.L. Hwang (1992) and S. Mallat and S. Zhong (1992)