Name
Abstract | ||
|---|---|---|
This paper looks at the effect of the number of vanishing moments on the approximation power of wavelet expansions. The Strang-Fix conditions imply that the error for an orthogonal wavelet approximation at scale a=2-i globally decays as aN, where N is the order of the transform. This is why, for a given number of scales, higher order wavelet transforms usually result in better signal approximations. We prove that this result carries over for the general biorthogonal case and that the rate of decay of the error is determined by the order properties of the synthesis scaling function alone. We also derive asymptotic error formulas and show that biorthogonal wavelet transforms are equivalent to their corresponding orthogonal projector as the scale goes to zero. These results strengthen Sweldens earlier analysis and confirm that the approximation power of biorthogonal and (semi-)orthogonal wavelet expansions is essentially the same. Finally, we compare the asymptotic performance of various wavelet transforms and briefly discuss the advantages of splines. We also indicate how the smoothness of the basis functions is beneficial in reducing the approximation error |
Year | DOI | Venue |
|---|---|---|
1996 | 10.1109/78.489025 | IEEE Transactions on Signal Processing |
Keywords | Field | DocType |
error statistics,signal processing,signal representation,smoothing methods,splines (mathematics),wavelet transforms,Strang-Fix conditions,approximation power,asymptotic error formulas,asymptotic performance,basis functions smoothness,biorthogonal wavelet expansions,higher order wavelet transforms,orthogonal projector,orthogonal wavelet approximation,semi-orthogonal wavelet expansions,signal approximations,splines,synthesis scaling function,vanishing moments | Orthogonal wavelet,Mathematical optimization,Mathematical analysis,Biorthogonal polynomial,Discrete wavelet transform,Cascade algorithm,Biorthogonal system,Wavelet packet decomposition,Mathematics,Biorthogonal wavelet,Wavelet | Journal |
Volume | Issue | ISSN |
44 | 3 | 1053-587X |
Citations | PageRank | References |
37 | 8.34 | 14 |
Authors | ||
1 | ||