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Sparse Signal Recovery With Minimization of 1-Norm Minus 2-Norm.
- Source :
-
IEEE Transactions on Vehicular Technology . Jul2019, Vol. 68 Issue 7, p6847-6854. 8p. - Publication Year :
- 2019
-
Abstract
- The key aim of compressed sensing is to stably recover a $K$ -sparse signals ${\boldsymbol{x}}$ from a linear model ${\boldsymbol{y}}=\boldsymbol{A}{\boldsymbol{x}}+\boldsymbol{v}$ , where $\boldsymbol{v}$ is a noise vector. Minimization of $\Vert {\boldsymbol{x}}\Vert _1-\Vert {\boldsymbol{x}}\Vert _2$ is a recently proposed effective recovery method. In this paper, we show that if the mutual coherence $\mu$ of $\boldsymbol{A}$ satisfies $\mu < \frac{1}{3K}$ , then this method can stably recover any $K$ -sparse signal ${\boldsymbol{x}}$ based on ${\boldsymbol{y}}$ and $\boldsymbol{A}$. As far as we know, this is the first sufficient condition based on mutual coherence for such method. [ABSTRACT FROM AUTHOR]
- Subjects :
- *COMPRESSED sensing
*WIRELESS sensor networks
*SPARSE matrices
Subjects
Details
- Language :
- English
- ISSN :
- 00189545
- Volume :
- 68
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Vehicular Technology
- Publication Type :
- Academic Journal
- Accession number :
- 137646171
- Full Text :
- https://doi.org/10.1109/TVT.2019.2919612