Naval Res. Lab., 4555 Overlook Ave., S.W., Bldg. 210, Washington, DC 20375-5000
Based on a wavelet auditory model (WAM) of the mammalian auditory system, discrete time-scale representations of acoustic signals which are inherently robust to ``noise'' emerge. The model consists of the two main processes of (i) a ``continuous'' wavelet transform with a causal analyzing wavelet determined by a ``shark-fin''-shaped frequency response (cochlear filter), and (ii) a specific and signal-dependent sampling of the wavelet transform. In general the pattern of samples in the wavelet domain is irregular and determined at lower frequencies by activity at higher frequencies. By analyzing the model in terms of the theory of mathematical frames, it is shown that acoustic signals may be fully recovered from their WAM representation through iterative reconstruction algorithms. Noise is thought of as that portion of an acoustic signal which is ``incoherent'' with respect to the underlying WAM frame functions. Because coherent energy is highly localized and incoherent (noise) energy is necessarily scattered in the time-scale plane by the WAM frame representation, wavelet shrinkage techniques provide powerful algorithms for noise suppression. Several numerical examples of the noise suppression abilities of these algorithms are presented in the paper.