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| Content Provider | Springer Nature Link |
|---|---|
| Author | Molter, Ursula Aldroubi, Akram Cabrelli, Carlos |
| Copyright Year | 2008 |
| Abstract | Given a set of vectors (the data) in a Hilbert space ℋ, we prove the existence of an optimal collection of subspaces minimizing the sum of the square of the distances between each vector and its closest subspace in the collection. This collection of subspaces gives the best sparse representation for the given data, in a sense defined in the paper, and provides an optimal model for sampling in union of subspaces. The results are proved in a general setting and then applied to the case of low dimensional subspaces of ℝ N and to infinite dimensional shift-invariant spaces in L 2(ℝ d ). We also present an iterative search algorithm for finding the solution subspaces. These results are tightly connected to the new emergent theories of compressed sensing and dictionary design, signal models for signals with finite rate of innovation, and the subspace segmentation problem. |
| Ending Page | 812 |
| Page Count | 20 |
| Starting Page | 793 |
| File Format | |
| ISSN | 10695869 |
| e-ISSN | 15315851 |
| Journal | Journal of Fourier Analysis and Applications |
| Issue Number | 5-6 |
| Volume Number | 14 |
| Language | English |
| Publisher | SP Birkhäuser Verlag Boston |
| Publisher Date | 2008-10-03 |
| Publisher Place | Boston |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Frames Signal, Image and Speech Processing Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.) Abstract Harmonic Analysis Sampling theory Fourier Analysis Sparsity Approximations and Expansions General harmonic expansions, frames Applications of Mathematics Sampling Compressed sensing Partial Differential Equations |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Analysis |
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