In this paper, two new sufficient conditions on stable recovery of the weighted signals via the weighted minimization are proposed based upon the weighted robust null space property (NSP) and the weighted restricted isometry property (RIP), respectively. Moreover, it is shown that the weighted RIP, as a stronger condition to estimate reconstruction errors, implies the weighted robust NSP.

中文翻译：

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加权问题稳定重构的充分条件

在本文中，分别基于加权鲁棒零空间特性（NSP）和加权受限等距特性（RIP），提出了通过加权最小化稳定恢复加权信号的两个新的充分条件。此外，它表明加权 RIP 作为估计重建误差的更强条件，意味着加权鲁棒 NSP。