Name
Abstract | ||
|---|---|---|
Shift-orthogonal wavelets are a new type of multiresolution wavelet bases that are orthogonal with respect to translation (or shifts) within one level but not with respect to dilations across scales. We characterize these wavelets and investigate their main properties by considering two general construction methods. In the first approach, we start by specifying the analysis and synthesis function spaces and obtain the corresponding shift-orthogonal basis functions by suitable orthogonalization. In the second approach, we take the complementary view and start from the digital filterbank. We present several illustrative examples, including a hybrid version of the Battle-Lemarie (1987, 1988) spline wavelets. We also provide filterbank formulas for the fast wavelet algorithm. A shift-orthogonal wavelet transform is closely related to an orthogonal transform that uses the same primary scaling function; both transforms have essentially the same approximation properties. One experimentally confirmed benefit of relaxing the interscale orthogonality requirement is that we can design wavelets that decay faster than their orthogonal counterpart |
Year | DOI | Venue |
|---|---|---|
1998 | 10.1109/78.700951 | IEEE Transactions on Signal Processing |
Keywords | Field | DocType |
filterbank formula,multiresolution wavelet base,corresponding shift-orthogonal basis function,shift-orthogonal wavelet,primary scaling function,digital filterbank,shift-orthogonal wavelet base,orthogonal counterpart,fast wavelet algorithm,synthesis function space,spline wavelet,wavelet transforms,spline,wavelet transform,wavelet analysis,filter bank,function space,shape,helium,signal reconstruction,biomedical imaging,approximation property,orthogonal transformation,finite impulse response filter,multiresolution analysis,band pass filters | Orthogonal wavelet,Mathematical optimization,Lifting scheme,Gabor wavelet,Legendre wavelet,Fast wavelet transform,Discrete wavelet transform,Mathematics,Wavelet,Wavelet transform | Journal |
Volume | Issue | ISSN |
46 | 7 | 1053-587X |
Citations | PageRank | References |
7 | 0.67 | 10 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Unser, M. | 1 | 3438 | 442.40 |
| Thevenaz, P. | 2 | 702 | 80.79 |
| A. Aldroubi | 3 | 1380 | 254.26 |