Achievable angles between two compressed sparse vectors under RIP-induced norm/distance constraints

Ling Hua Chang, Jwo-Yuh Wu

研究成果同行評審

1 引文 斯高帕斯(Scopus)

摘要

The angle between two compressed sparse vectors subject to the norm/distance constraints imposed by the restricted isometry property (RIP) of the sensing matrix plays an important role in the studies of many compressive sensing (CS) problems. Assuming that (i) u and v are two sparse vectors with {measured angle}(u, v) = θ and (ii) the sensing matrix Φ satisfies RIP, this paper is aimed at analytically characterizing the achievable angles between Φu and Φv. Motivated by geometric interpretations of RIP and with the aid of the well-known law of cosines, we propose a plane geometry based formulation for the study of the considered problem. It is shown that all the RIP-induced norm/distance constraints on Φu and Φv can be jointly depicted via a simple geometric diagram in the two-dimensional plane. This allows for a joint analysis of all the involved algebraic constraints from a geometric perspective. By conducting plane geometry analyses based on the constructed diagram, closed-form formulae for the maximal and minimal achievable angles are derived. Computer simulations confirm that the proposed solution is tighter than an existing algebraic-based estimate derived using the polarization identity.

原文English
頁面523-528
頁數6
DOIs
出版狀態Published - 2014
事件2014 International Conference on Computing, Networking and Communications, ICNC 2014 - Honolulu, HI, 美國
持續時間: 3 2月 20146 2月 2014

Conference

Conference2014 International Conference on Computing, Networking and Communications, ICNC 2014
國家/地區美國
城市Honolulu, HI
期間3/02/146/02/14

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