Zero-Crossings of a Wavelet Transform

Abstract

Sharp variation points are among the most mean ingful features for characterizing transient signals. For a particular class of wavelets, the zero-crossings of a wavelet transform provide the locations of the signal sharp variation points at different scales. The completeness and stability of a signal representation based on zero-crossings of a wavelet transform at the scales 2 j, for integer j are studied. An alternative projection algorithm is described. It reconstructs a signal from a zero-crossing representation which is stabilized. The reconstruction algorithm has a fast convergence and each iteration requires O(N log 2 (N) computations for a signal of N samples. The zero-crossings of a wavelet transform define a representation which is well adapted for solving pattern recognition problems. As an example, the implementation and results of a coarse-to-fine stereo-matching algorithm are described. © 1991 IEEE