Name
Abstract | ||
|---|---|---|
Recently, a nonconvex relaxation of low-rank matrix recovery (LMR), called the Schatten- $p$ quasi-norm minimization ($0< p< 1$), was introduced instead of the previous nuclear norm minimization in order to approximate the problem of LMR closer. In this paper, we introduce a notion of the restricted $p$-isometry constants ( $0< p\\leq 1$) and derive a $p$ -RIP condition for exact reconstruction of LMR via Schatten-$p$ quasi-norm minimization. In particular, we determine how many random, Gaussian measurements are needed for the $p$-RIP condition to hold with high probability, which gives a theoretical result that it needs fewer measurements with small $p$ for exact recovery via Schatten- $p$ quasi-norm minimization than when $p=1$. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1109/TIT.2013.2250577 | IEEE Transactions on Information Theory |
Keywords | Field | DocType |
Gaussian processes,approximation theory,concave programming,matrix algebra,minimisation,probability,Gaussian measurements,LMR reconstruction,Schatten- p quasinorm minimization,approximation,low-rank matrix recovery,nonconvex matrix recovery,nuclear norm minimization,p -RIP condition,probability,restricted p-isometry constants,restricted p-isometry properties,Low-rank matrix recovery (LMR),Schatten-$p$ quasi-norm minimization,random Gaussian linear transformation,restricted $p$-isometry constants | Discrete mathematics,Combinatorics,Matrix (mathematics),Matrix decomposition,Isometry,Approximation theory,Minimisation (psychology),Gaussian,Gaussian process,Linear map,Mathematics | Journal |
Volume | Issue | ISSN |
59 | 7 | 0018-9448 |
Citations | PageRank | References |
15 | 0.60 | 11 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Min Zhang | 1 | 27 | 17.07 |
| Zheng-Hai Huang | 2 | 350 | 29.66 |
| Ying Zhang | 3 | 163 | 25.25 |