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 2014 → 6 2月 2014 |
Conference
Conference | 2014 International Conference on Computing, Networking and Communications, ICNC 2014 |
---|---|
國家/地區 | 美國 |
城市 | Honolulu, HI |
期間 | 3/02/14 → 6/02/14 |