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In the context of compressed sensing, the nonconvex lq minimization with 0 &lt;; q &lt;; 1 has been studied in recent years. In this letter, by generalizing the sharp bound for l1 minimization of Cai and Zhang, we show that the condition &#x03C3;(sq+1)k &lt;; 1/&#x221A;(sq-2+1) in terms of restricted isometry constant (RIC) can guarantee the exact recovery of k-sparse signals in the noiseless case and the stable recovery of approximately k-sparse signals in the noisy case by lq minimization. This result is more general than the sharp bound for l1 minimization when the order of RIC is greater than 2k and illustrates the fact that a better approximation to l0 minimization is provided by lq minimization than that provided by l1 minimization.

ieee signal processing letters

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