Concentration of S-largest mutilated vectors with -quasinorm for and its applications

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• 作者：Yi Cen ; Rentao Gu ; Yuefeng Ji
• 关键词：Compressive sensing ; Null space of sensing matrix ; S-largest mutilated vector ; Concentration with lp-quasinorm ; Restricted isometry constant ¦ÄS(¦µ) ; Exact recovery via (lp) minimization
• 刊名：Applied Mathematics and Computation
• 出版年：2012
• 出版时间：15 October, 2012
• 年：2012
• 卷：219
• 期：3
• 页码：1087-1092
• 全文大小：182 K

文摘

Suppose is a known sensing matrix. For any nonzero vector in the null space of and any given positive integer , we further introduce a definition of S-largest mutilated vector of and develop some of its important properties associated with the concept of concentration in space () based on the concept of concentration proposed by Donoho in compressive sensing. As application of these important properties, we assert that any S-sparse signal can be exactly recovered via () minimization in the noiseless case as soon as the concentration of S-largest mutilated vectors with -quasinorm is less than 1/2. This is a complement and generalization for a similar result proposed by Donoho. Moreover, the upper bound condition of proposed by Cai for exact recovery of sparse signals via () minimization is also derived from this result simply.