New RIC Bounds via l_q-minimization with 0
The restricted isometry constants (RICs) play an important role in exact recovery theory of sparse signals via l_q(0
restricted isometry constant
New RIC Bounds via l_q-minimization with 0
Improved Bounds for RIC in Compressed Sensing
This paper improves bounds for restricted isometry constant (RIC) in compressed sensing. Let \phi be a m*n real matrix and k be a positive integer with k
On RIC bounds of Compressed Sensing Matrices for Approximating Sparse Solutions Using Lq Quasi Norms
This paper follows the recent discussion on the sparse solution recovery with quasi-norms Lq; q\in(0,1) when the sensing matrix possesses a Restricted Isometry Constant \delta_{2k} (RIC). Our key tool is an improvement on a version of “the converse of a generalized Cauchy-Schwarz inequality” extended to the setting of quasi-norm. We show that, if \delta_{2k}\le 1/2, … Read more
Sufficient Conditions for Low-rank Matrix Recovery,Translated from Sparse Signal Recovery
The low-rank matrix recovery (LMR) is a rank minimization problem subject to linear equality constraints, and it arises in many fields such as signal and image processing, statistics, computer vision, system identification and control. This class of optimization problems is $NP$-hard and a popular approach replaces the rank function with the nuclear norm of the … Read more
Exact Low-rank Matrix Recovery via Nonconvex Mp-Minimization
The low-rank matrix recovery (LMR) arises in many fields such as signal and image processing, statistics, computer vision, system identification and control, and it is NP-hard. It is known that under some restricted isometry property (RIP) conditions we can obtain the exact low-rank matrix solution by solving its convex relaxation, the nuclear norm minimization. In … Read more
New Bounds for Restricted Isometry Constants in Low-rank Matrix Recovery
In this paper, we establish new bounds for restricted isometry constants (RIC) in low-rank matrix recovery. Let $\A$ be a linear transformation from $\R^{m \times n}$ into $\R^p$, and $r$ the rank of recovered matrix $X\in \R^{m \times n}$. Our main result is that if the condition on RIC satisfies $\delta_{2r+k}+2(\frac{r}{k})^{1/2}\delta_{\max\{r+\frac{3}{2}k,2k\}}