Name
Abstract | ||
|---|---|---|
We present a generalization of the orthonormal Daubechies wavelets and of their related biorthogonal flavors (Cohen-Daubechies-Feauveau, 9/7). Our fundamental constraint is that the scaling functions should reproduce a predefined set of exponential polynomials. This allows one to tune the corresponding wavelet transform to a specific class of signals, thereby ensuring good approximation and sparsity properties. The main difference with the classical construction of Daubechies is that the multiresolution spaces are derived from scale-dependent generating functions. However, from an algorithmic standpoint, Mallat's fast wavelet transform algorithm can still be applied; the only adaptation consists in using scale-dependent filter banks. Finite support ensures the same computational efficiency as in the classical case. We characterize the scaling and wavelet filters, construct them and show several examples of the associated functions. We prove that these functions are square-integrable and that they converge to their classical counterparts of the corresponding order. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1109/TSP.2007.896255 | IEEE Transactions on Signal Processing |
Keywords | Field | DocType |
scale-dependent filter bank,corresponding wavelet,orthonormal daubechies wavelet,generalized daubechies wavelet families,scale-dependent generating function,corresponding order,classical construction,wavelet filter,fast wavelet,classical counterpart,classical case,indexing terms,wavelet transform,fast wavelet transform,wavelet transforms,orthonormal,exponential polynomial,spline,filter bank,exponential polynomials,polynomials,biorthogonal,reproduction,generating function,signal processing,wavelet | Mathematical optimization,Coiflet,Multiresolution analysis,Discrete wavelet transform,Daubechies wavelet,Cascade algorithm,Wavelet packet decomposition,Mathematics,Wavelet,Wavelet transform | Journal |
Volume | Issue | ISSN |
55 | 9 | 1053-587X |
Citations | PageRank | References |
11 | 0.78 | 7 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| C. Vonesch | 1 | 224 | 17.13 |
| T Blu | 2 | 2574 | 259.70 |
| Unser, M. | 3 | 3438 | 442.40 |