A Nonclassical LIL for Geometrically Weighted Series in Banach Space

We consider efficient methods for the recovery of block sparse signals from underdetermined system of linear equations. We show that if the measurement matrix satisfies the block RIP with δ2s 〈 0.4931, then every block s-sparse signal can be recovered through the proposed mixed l2/ll-minimization ap...

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Bibliographic Details
Published in:Acta mathematica Sinica. English series 2013-07, Vol.29 (7), p.1413-1420
Main Authors: Fu, Ke Ang, Yang, Xiao Rong, Huang, Wei
Format: Article
Language:English
Subjects:
Algebra
Approximation
Asymptotic properties
Banach
Banach space
Banach spaces
Constants
Equivalence
Geometry
IEEE
Infinity
Mathematics
Mathematics and Statistics
Random variables
Studies
Theorems
Topology
充分条件
加权系
测量矩阵
空间几何
线性方程
非经典
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Summary:We consider efficient methods for the recovery of block sparse signals from underdetermined system of linear equations. We show that if the measurement matrix satisfies the block RIP with δ2s 〈 0.4931, then every block s-sparse signal can be recovered through the proposed mixed l2/ll-minimization approach in the noiseless case and is stably recovered in the presence of noise and mismodeling error. This improves the result of Eldar and Mishali （in IEEE Trans. Inform. Theory 55： 5302-5316, 2009）. We also give another sufficient condition on block RIP for such recovery method： 58 〈 0.307.
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-013-1591-8