Wavelets on Irregular Grids with Arbitrary Dilation Matrices, and Frames Atoms for L^2(R^d)
| dc.creator | Aldroubi, Akram | |
| dc.creator | Cabrelli, Carlos | |
| dc.creator | Molter, Ursula M. | |
| dc.date | 2007-03-14 | |
| dc.date.accessioned | 2026-07-07T07:52:05Z | |
| dc.date.available | 2026-07-07T07:52:05Z | |
| dc.description | In this article, we develop a general method for constructing wavelets {|det A_j|^{1/2} g(A_jx-x_{j,k}): j in J, k in K}, on irregular lattices of the form X={x_{j,k} in R^d: j in J, k in K}, and with an arbitrary countable family of invertible dxd matrices {A_j in GL_d(R): j in J} that do not necessarily have a group structure. This wavelet construction is a particular case of general atomic frame decompositions of L^2(R^d) developed in this article, that allow other time frequency decompositions such as non-harmonic Gabor frames with non-uniform covering of the Euclidean space R^d. Possible applications include image and video compression, speech coding, image and digital data transmission, image analysis, estimations and detection, and seismology. | |
| dc.description | 23 pages, 3 figures, some small correction after publication | |
| dc.identifier | https://arxiv.org/abs/math/0703438 | |
| dc.identifier | http://arxiv.org/abs/math/0703438 | |
| dc.identifier | Applied and Computational Harmonic Analysis 17, 2004, pgs 119-140 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/125752 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 42C40 | |
| dc.title | Wavelets on Irregular Grids with Arbitrary Dilation Matrices, and Frames Atoms for L^2(R^d) | |
| dc.type | text |