Abstract
This paper presents novel results concerning the recovery of approximately k-sparse signals in noisy cases. Under some restricted assumptions on the constraint constant in the ℓp (0 < p ≤ 1) minimization model, Chen and the author of this paper analyzed the recovery of approximately k-sparse signals in [10]. In this paper, these requirements are successfully removed, and the stable recovery of approximately k-sparse signals in two common noisy settings is both proved under a general RIP condition via ℓp minimization. Meanwhile, the reconstruction error bounds are characterized, which scale well with the noise bound and the non-sparsity of the original signal. Moreover, the newly derived estimations of reconstruction error are demonstrated to be much tighter than the existing ones.
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