| Autor: |
Changlong Wang, Jigen Peng |
| Jazyk: |
angličtina |
| Rok vydání: |
2018 |
| Předmět: |
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| Zdroj: |
Journal of Inequalities and Applications, Vol 2018, Iss 1, Pp 1-18 (2018) |
| Druh dokumentu: |
article |
| ISSN: |
1029-242X |
| DOI: |
10.1186/s13660-017-1601-y |
| Popis: |
Abstract The joint sparse recovery problem is a generalization of the single measurement vector problem widely studied in compressed sensing. It aims to recover a set of jointly sparse vectors, i.e., those that have nonzero entries concentrated at a common location. Meanwhile l p $l_{p}$ -minimization subject to matrixes is widely used in a large number of algorithms designed for this problem, i.e., l 2 , p $l_{2,p}$ -minimization min X ∈ R n × r ∥ X ∥ 2 , p s.t. A X = B . $$\begin{aligned} \min_{X \in\mathbb {R}^{n\times r}} \Vert X \Vert _{2,p}\quad \text{s.t. }AX=B. \end{aligned}$$ Therefore the main contribution in this paper is two theoretical results about this technique. The first one is proving that in every multiple system of linear equations there exists a constant p ∗ $p^{\ast}$ such that the original unique sparse solution also can be recovered from a minimization in l p $l_{p}$ quasi-norm subject to matrixes whenever 0 < p < p ∗ $0< p |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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