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
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
This method reduces the reconstruction problem to that of solving a
system of linear algebraic equations.
Get the full paper (without figures): PDF file.
Get the figures of the paper: PDF file.
Get the official version via doi:10.1109/78.258102.
Get the erratum: PDF file.
Get the official version of erratum via doi:10.1109/TSP.1997.558499.
me if you have any comments or questions!
back to Naoki's Publication Page