Multiresolution representations using the autocorrelation functions of compactly supported wavelets

Author

Saito, Naoki ; Beylkin, Gregory

Volume

41

Issue

12

fYear

1993

fDate

12/1/1993 12:00:00 AM

Firstpage

3584

Lastpage

3590

Abstract

Proposes a shift-invariant multiresolution representation of signals or images using dilations and translations of the autocorrelation 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, the present 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. The authors also develop a noniterative method for reconstructing signals from their zero-crossings (and slopes at these zero-crossings) in their representation. This method reduces the reconstruction problem to that of solving a system of linear algebraic equations

Keywords

correlation methods; image reconstruction; interpolation; iterative methods; signal processing; wavelet transforms; algorithm; associated iterative interpolation schemes; autocorrelation functions; compactly supported wavelets; dilations; image reconstruction; linear algebraic equations; multiscale edges; noniterative method; reconstruction problem; shift-invariance; shift-invariant multiresolution representation; signal reconstruction; symmetric analyzing functions; translations; zero-crossings; Algorithm design and analysis; Autocorrelation; Equations; Image edge detection; Image reconstruction; Image resolution; Interpolation; Iterative algorithms; Signal resolution; Wavelet analysis;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.258102

Filename

258102