The Bounds Of RIC For Low Rank Matrices Recovery

In many real applications, it has been shown in practice that various signals of interest may be (approximately) sparsely modeled, and that sparse modeling is often beneficial. A rich theory of sparse and compressible signal recovery has recently been developed under the names compressed sensing. This revolutionary research has demonstrated that many signals can be recovered from severely un-dersampled measurements by taking advantage of their inherent low-dimensional structure. More recently, an okshoot of CS has been a focus of research matrices of low rank. Low-rank matrix recovery (LRMR) is demonstrating a rapidly growing array of important applications such as quantum state tomography, recommender systems, and system identification and control.In this paper, we first discussed the problem that recover signals with partial support known. We focus on the case that the known information on support set is exact and gave the sufficient condition via RIP to guarantee the exact recovery and discussed the noisy case. Our results improved the results in [70]. Next we investigated the theory of low rank matrices recovery as following:●Give some decay properties of the restricted isometry constants of linear en-semble:●Provide the upper bounds of restricted isometry constants to guarantee the exact recovery for low rank matrices and the stability analysis. We proved that if (δ2r≥1/(?) or δr≥1/3, then there exist some matrix with rank at most r which cannot be exactly recovered by nuclear norm minimization.●Improve the bounds of restricted isometry constants for the stability analysis for the matrix Dantzig selector and Lasso algorithm.●Provide the bounds of restricted isometry constants to guarantee the low rank matrices recovered exactly by solving Schatten p (0<p<1) quasi norm minimization problem.