Restrictedp-Isometry Properties of Partially Sparse Signal Recovery

Restricted p-Isometry Properties of Partially Sparse Signal Recovery

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

On Partially Sparse Recovery

In this paper we consider the problem of recovering a partially sparse solution of an underdetermined system of linear equations by minimizing the `1-norm of the part of the solution vector which is known to be sparse. Such a problem is closely related to the classical problem in Compressed Sensing where the `1-norm of the whole solution vector is minimized. We introduce analogues of restricted...

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 ...

On the gap between restricted isometry properties and sparse recovery conditions

We consider the problem of recovering sparse vectors from underdetermined linear measurements via `pconstrained basis pursuit. Previous analyses of this problem based on generalized restricted isometry properties have suggested that two phenomena occur if p 6= 2. First, one may need substantially more than s log(en/s) measurements (optimal for p = 2) for uniform recovery of all s-sparse vectors...