Name
Abstract | ||
|---|---|---|
Generalized orthogonal matching pursuit (gOMP), also called orthogonal multi-matching pursuit, is an extension of OMP in the sense that $N\geq 1$ indices are identified per iteration. In this letter, we show that if the restricted isometry constant $\delta _{NK+1}$ of a sensing matrix $\boldsymbol {A}$ satisfies $\delta _{NK+1} < 1/ {(K/N+1)}^{1/2}$ , then under a condition on the signal-to-noise ratio, gOMP identifies at least one index in the support of any $K$ -sparse signal ${\boldsymbol {x}}$ from ${\boldsymbol {y}}= \boldsymbol {A} {\boldsymbol {x}} + \boldsymbol {v}$ at each iteration, where $\boldsymbol {v}$ is a noise vector. Surprisingly, this condition does not require $N\leq K$ which is needed in Wang et al. and Liu et al. Thus, $N$ can have more choices. When $N=1$ , it reduces to be a sufficient condition for OMP, which is less restrictive than that proposed in Wang et al. Moreover, in the noise-free case, it is a sufficient condition for accurately recovering ${\boldsymbol {x}}$ in $K$ iterations, which is less restrictive than the best known one. In particular, it reduces to the sharp condition proposed in Mo 2015 when $N=1$ . |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1109/LCOMM.2016.2642922 | IEEE Communications Letters |
Keywords | Field | DocType |
Matching pursuit algorithms,Signal to noise ratio,Mars,Indexes,Sensors,Noise measurement,Electronic mail | Matching pursuit,Discrete mathematics,Mathematical optimization,Combinatorics,Matrix (mathematics),Isometry,Mathematics | Journal |
Volume | Issue | ISSN |
21 | 4 | 1089-7798 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| jinming wen | 1 | 103 | 14.52 |
| Zhengchun Zhou | 2 | 717 | 53.78 |
| Dongfang Li | 3 | 106 | 15.34 |
| Xiaohu Tang | 4 | 1294 | 121.15 |