MULTIRESOLUTION REPRESENTATIONS USING THE AUTOCORRELATION FUNCTIONS OF COMPACTLY SUPPORTED WAVELETS

We propose a shift-invariant multiresolution representation of signals or images using dilations and translations of the autocorrelation fun ctions of compactly supported wavelets. Although these functions do no t form an orthonormal basis, their properties make them useful for sig nal and image analysis. Unlike wavelet-based orthonormal representatio ns, our representation has 1) symmetric analyzing functions, 2) shift- invariance, 3) associated iterative interpolation schemes, and 4) a si mple algorithm for finding the locations of the multiscale edges as ze ro-crossings. We also develop a noniterative method for reconstructing signals from their zero-crossings (and slopes at these zero-crossings ) in our representation. This method reduces the reconstruction proble m to that of solving a system of linear algebraic equations.