Multiresolution representations using the auto-correlation functions of compactly supported wavelets, (with G. Beylkin), IEEE Trans. Signal Processing, vol.41, no.12, pp.3584-3590, 1993; Erratum: vol.45, no.3, p.768, 1997.


We propose a shift-invariant multiresolution representation of signals or images using dilations and translations of the auto-correlation functions of compactly supported wavelets. Although these functions do not form an orthonormal basis, their properties make them useful for signal and image analysis. Unlike wavelet-based orthonormal representations, our representation has (1) symmetric analyzing functions, (2) shift-invariance, (3) associated iterative interpolation schemes, and (4) a simple algorithm for finding the locations of the multiscale edges as zero-crossings. We also develop a non-iterative method for reconstructing signals from their zero-crossings (and slopes at these zero-crossings) in our representation. This method reduces the reconstruction problem to that of solving a system of linear algebraic equations.

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  • Get the official version via doi:10.1109/78.258102.
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  • Get the official version of erratum via doi:10.1109/TSP.1997.558499.

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