The Dantzig selector: recovery of signal via ℓ 1 − αℓ 2 minimization

In the paper, we proposed the Dantzig selector based on the ℓ 1 − αℓ 2 (0 < α ⩽ 1) minimization for the signal recovery. In the Dantzig selector, the constraint ‖ A ⊤ ( b − Ax )‖∞ ⩽ η for some small constant η > 0 means the columns of A has very weakly correlated with the error vector e = Ax − b . First, recovery guarantees based on the restricted isometry property are established for signals. Next, we propose the effective algorithm to solve the proposed Dantzig selector. Last, we illustrate the proposed model and algorithm by extensive numerical experiments for the recovery of signals in the cases of Gaussian, impulsive and uniform noises. And the performance of the proposed Dantzig selector is better than that of the existing methods.

Sparse phase retrieval via ℓp (0 < p ≤ 1) minimization

In this paper, the [Formula: see text]-analysis model for the phase retrieval problem of sparse unknown signals in the redundant dictionary is extended to the [Formula: see text]-analysis model, where [Formula: see text]. It’s shown that if the measurement matrix [Formula: see text] satisfies the strong restricted isometry property adapted to D (S-DRIP) condition, the unknown signal [Formula: see text] can be stably recovered by analyzing the [Formula: see text] [Formula: see text] minimization model.

A New Analysis for Support Performance with Block Generalized Orthogonal Matching Pursuit

For recovering block-sparse signals with unknown block structures using compressive sensing, a block orthogonal matching pursuit- (BOMP-) like block generalized orthogonal matching pursuit (BgOMP) algorithm has been proposed recently. This paper focuses on support conditions of recovery of any K -sparse block signals incorporating BgOMP under the framework of restricted isometry property (RIP). The proposed support conditions guarantee that BgOMP can achieve accurate recovery block-sparse signals within k iterations.