Sparse Signal Recovery by <formula formulatype="inline"> <tex Notation="TeX">${\ell_q}$</tex></formula> Minimization Under Restricted Isometry Property

Sparse signal recovery by $\ell_q$ minimization under restricted isometry property

In the context of compressed sensing, the nonconvex lq minimization with 0 < q < 1 has been studied in recent years. In this paper, by generalizing the sharp bound for l1 minimization of Cai and Zhang, we show that the condition δ(sq+1)k < 1

The Restricted Isometry Property and ` sparse recovery failure

This paper considers conditions based on the restricted isometry constant (RIC) under which the solution of an underdetermined linear system with minimal ` norm, 0 < p ≤ 1, is guaranteed to be also the sparsest one. Specifically matrices are identified that have RIC, δ2m, arbitrarily close to 1/ √ 2 ≈ 0.707 where sparse recovery with p = 1 fails for at least one m-sparse vector. This indicates ...

Restricted p-Isometry Properties of Partially Sparse Signal Recovery

A Generalized Restricted Isometry Property

Compressive Sampling (CS) describes a method for reconstructing high-dimensional sparse signals from a small number of linear measurements. Fundamental to the success of CS is the existence of special measurement matrices which satisfy the so-called Restricted Isometry Property (RIP). In essence, a matrix satisfying RIP is such that the lengths of all sufficiently sparse vectors are approximate...

Orthogonal Matching Pursuit under the Restricted Isometry Property

This paper is concerned with the performance of Orthogonal Matching Pursuit (OMP) algorithms applied to a dictionary D in a Hilbert space H. Given an element f ∈ H, OMP generates a sequence of approximations fn, n = 1, 2, . . ., each of which is a linear combination of n dictionary elements chosen by a greedy criterion. It is studied whether the approximations fn are in some sense comparable to...