Title :
On the Constrained Minimal Singular Values for Sparse Signal Recovery
Author :
Zhang, Hui ; Cheng, Lizhi
Author_Institution :
Dept. of Math. & Syst. Sci., Nat. Univ. of Defense Technol., Changsha, China
Abstract :
The l1 -constrained minimal singular value (l1-CMSV) of the sensing matrix for sparse signal recovery is investigated in this letter. By exploiting certain geometrical properties of the (l_1-CMSV), we derive new sufficient conditions for the recovery of both exactly and approximately sparse signals. Moreover, we demonstrate that a class of structured random matrices, including the Fourier random matrices and the Hadamard random matrices, can satisfy these sufficient conditions by showing their l_1-CMSV are bounded away from zero with high probability, as long as the number of measurements is reasonably large.
Keywords :
Fourier transforms; Hadamard transforms; probability; signal processing; sparse matrices; CMSV; Fourier random matrices; Hadamard random matrices; constrained minimal singular values; geometrical properties; probability; sensing matrix; sparse signal recovery; structured random matrices; Compressed sensing; Educational institutions; Level set; Sensors; Signal reconstruction; Sparse matrices; Vectors; $l_{1}$-constrained minimal singular value; sparse recovery; structured random matrices; width of $l_{1}$ -truncated set;
Journal_Title :
Signal Processing Letters, IEEE
DOI :
10.1109/LSP.2012.2203802
