The null space property of the weighted l_r - l₁ minimization

The null space property (NSP), which relies merely on the null space of the sensing matrix column space, has drawn numerous interests in sparse signal recovery. This paper studies NSP of the weighted l(r) - l(1) (r ? (0, 1]) minimization. Several versions of NSP of the weighted l(r) - l(1) minimization including the weighted l(r) - l(1) NSP, the weighted l(r) - l(1) stable NSP, the weighted l(r) - l(1) robust NSP and the l(q) weighted l(r) - l(1) robust NSP for 1 = q = 2, are proposed, as well as the associating considerable results are derived. Under these NSPs, sufficient conditions for the recovery of (sparse) signals with the weighted l(r) - l(1) minimization are established. Furthermore, we show that to some extent, the weighted l(r) - l(1) stable NSP is weaker than the restricted isometric property (RIP). And the RIP condition we obtained is better than that of Zhou (2022).