On the perturbation of measurement matrix in non-convex compressed sensing

A perturbation analysis of nonconvex block-sparse compressed sensing

“…Especially, when p → 0 (a > 1), we can get the BRIP condition δ 2K < 2 (1+ǫ (2aK) A ) 2 − 1 for recovery of block K-sparse signals via the mixed ℓ 2 /ℓ 0 minimization, as we know, the best sufficient condition on RIP is δ 2K < 1 to guarantee exact reconstruction of sparse signals by ℓ 0 minimization ( [20]), so our results generalize that condition to the setting of existing noise and block-sparse signals. In addition, as a special case of Theorem 1, d 1 = d 2 = · · · = d m = 1, our results degenerate to the conventional CS, which has been proved in [16].…”

“…Condition (9) of the Theorem generalizes the condition of ℓ p case in [16] to the mixed ℓ 2 /ℓ p minimization. Note that the right hand side of (9) monotonically decreases with p,…”

“…Proof of the theorem The idea of the proof is similar to that in the literature [16,17]. Let z * = x + h be a solution of (5), where x is the original signal we need to recover.…”

“…In [18], Herman and Strohmer derived a restricted isometry property condition to recover stably the signal x by (3). In 2014, Ince and Nacaroglu( [16]) proposed the following completely perturbed ℓ p (0 < p < 1) minimization to reconstruct the signal, i.e.,…”

Fast non‐convex compressed sensing approach for diagnosis of defective array elements using planar near‐field measurements

“…However, as discussed in the introduction, the solution of problem (6) is affected by local minima. In this study, instead of using the perturbation technique proposed in [28] to overcome this limitation, the IRLS method is chosen as the candidate solver to find the solution of (7), in which ℓ p objective function is replaced by a weighted ℓ 2 norm [34]…”