Name
Abstract | ||
|---|---|---|
A construction for providing single dyadic orthonormal wavelets in Euclidean space ℝd is given. It is called the general neighborhood mapping construction. The fact that one wavelet is sufficient to generate an orthonormal basis for L2(ℝd) is the critical issue. The validity of the construction is proved, and the construction is implemented computationally to
provide a host of examples illustrating various geometrical properties of such wavelets in the spectral domain. Because of
the inherent complexity of these single orthonormal wavelets, the method is applied to the construction of single dyadic tight
frame wavelets, and these tight frame wavelets can be surprisingly simple in nature. The structure of the spectral domains
of the wavelets arising from the general neighborhood mapping construction raises a basic geometrical question. There is also
the question of whether or not the general neighborhood mapping construction gives rise to all single dyadic orthonormal wavelets.
Results are proved giving partial answers to both of these questions. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1007/s10444-004-7623-2 | Adv. Comput. Math. |
Keywords | Field | DocType |
frames,wavelets | Mathematical analysis,Gabor wavelet,Legendre wavelet,Euclidean space,Orthonormal basis,Orthonormal wavelets,Mathematics,Tight frame,Wavelet transform,Wavelet | Journal |
Volume | Issue | ISSN |
24 | 1-4 | 1019-7168 |
Citations | PageRank | References |
2 | 0.70 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| John J. Benedetto | 1 | 132 | 16.90 |
| Songkiat Sumetkijakan | 2 | 2 | 1.38 |