Name
Title | ||
|---|---|---|
Tensor restricted isometry property analysis for a large class of random measurement ensembles |
Abstract | ||
|---|---|---|
In previous work, theoretical analysis based on the tensor Restricted Isometry Property (t-RIP) established the robust recovery guarantees of a low-tubal-rank tensor. The obtained sufficient conditions depend strongly on the assumption that the linear measurement maps satisfy the t-RIP. In this paper, by exploiting the probabilistic arguments, we prove that such linear measurement maps exist under suitable conditions on the number of measurements in terms of the tubal rank r and the size of third-order tensor n1, n2, n3. And the obtained minimal possible number of linear measurements is nearly optimal compared with the degrees of freedom of a tensor with tubal rank r. Specially, we consider a random sub-Gaussian distribution that includes Gaussian, Bernoulli and all bounded distributions and construct a large class of linear maps that satisfy a t-RIP with high probability. Moreover, the validity of the required number of measurements is verified by numerical experiments. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1007/s11432-019-2717-4 | SCIENCE CHINA-INFORMATION SCIENCES |
DocType | Volume | Issue |
Journal | 64 | 1 |
ISSN | Citations | PageRank |
1674-733X | 1 | 0.34 |
References | Authors | |
0 | 5 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Feng Zhang | 1 | 11 | 5.93 |
| Wendong Wang | 2 | 10 | 3.19 |
| Jingyao Hou | 3 | 1 | 1.02 |
| Jianjun Wang | 4 | 53 | 11.84 |
| Jianwen Huang | 5 | 4 | 2.40 |