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- Title
Generalized notions of sparsity and restricted isometry property. Part I: a unified framework.
- Authors
Junge, Marius; Lee, Kiryung
- Abstract
The restricted isometry property (RIP) is an integral tool in the analysis of various inverse problems with sparsity models. Motivated by the applications of compressed sensing and dimensionality reduction of low-rank tensors, we propose generalized notions of sparsity and provide a unified framework for the corresponding RIP, in particular when combined with isotropic group actions. Our results extend an approach by Rudelson and Vershynin to a much broader context including commutative and non-commutative function spaces. Moreover, our Banach space notion of sparsity applies to affine group actions. The generalized approach in particular applies to high-order tensor products.
- Subjects
RESTRICTED isometry property; NONCOMMUTATIVE function spaces; TENSOR products; INVERSE problems; BANACH spaces
- Publication
Information & Inference: A Journal of the IMA, 2020, Vol 9, Issue 1, p157
- ISSN
2049-8764
- Publication type
Article
- DOI
10.1093/imaiai/iay018