The Dantzig Selector: Sparse Signals Recovery via l_p-q Minimization

TL;DR

This paper introduces the Dantzig selector using l_{p-q} minimization for sparse signal recovery, providing theoretical guarantees and graphical illustrations of conditions under which recovery is successful.

Contribution

It develops a new sparse recovery method based on l_{p-q} minimization and establishes theoretical guarantees using restricted isometry properties.

Findings

Convex combination representation of sparse vectors under l_{p-q} minimization

Recovery guarantees based on restricted isometry property frames

Graphical illustrations of sufficient conditions for signal recovery

Abstract

In the paper, we proposed the Dantzig selector based on the $l_{p-q}$ ($0<p\leq1, 1<q\leq2$) minimization for the signal recovery. First, we establish the convex combination representation of sparse vectors under the $l_{p-q}$ minimization problem. Next, we give the signal recovery guarantees that based on two classes of restricted isometry property frames. Last, some graphical illustrations are presented for the sufficient conditions of the signal recovery.