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Compressed Data Separation via ℓq-Split Analysis with ℓ∞-Constraint.
- Source :
-
Acta Mathematica Sinica . Jul2024, Vol. 40 Issue 7, p1655-1673. 19p. - Publication Year :
- 2024
-
Abstract
- In this paper, we study compressed data separation (CDS) problem, i.e., sparse data separation from a few linear random measurements. We propose the nonconvex ℓq-split analysis with ℓ∞-constraint and 0 < q ≤ 1. We call the algorithm ℓq-split-analysis Dantzig selector (ℓq-split-analysis DS). We show that the two distinct subcomponents that are approximately sparse in terms of two different dictionaries could be stably approximated via the ℓq-split-analysis DS, provided that the measurement matrix satisfies either a classical D-RIP (Restricted Isometry Property with respect to Dictionaries and ℓ2 norm) or a relatively new (D, q)-RIP (RIP with respect to Dictionaries and ℓq-quasi norm) condition and the two different dictionaries satisfy a mutual coherence condition between them. For the Gaussian random measurements, the measurement number needed for the (D, q)-RIP condition is far less than those needed for the D-RIP condition and the (D, 1)-RIP condition when q is small enough. [ABSTRACT FROM AUTHOR]
- Subjects :
- *LENGTH measurement
*ENCYCLOPEDIAS & dictionaries
Subjects
Details
- Language :
- English
- ISSN :
- 14398516
- Volume :
- 40
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Acta Mathematica Sinica
- Publication Type :
- Academic Journal
- Accession number :
- 178593784
- Full Text :
- https://doi.org/10.1007/s10114-024-2083-8