Signal representation using wavelet transform modulus maxima

We examine the representation of signals by the wavelet transform modulus maxima together with the alternating projection reconstruction algorithm proposed by Mallat. We show that the projection algorithm of Mallat (see IEEE Trans. Patt. Anal. Mach. Intell., vol.14, p.710-732, July 1992, and IEEE Trans. Inform. Theory, vol.38, p.617-643, March 1992) is not minimum distance and not necessarily nonexpansive. Convergence is therefore not guaranteed. We describe an alternative projection operator which is minimum distance and nonexpansive and show that it is monotonically converging.<>