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- W2034954715 abstract "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 (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." @default.
- W2034954715 created "2016-06-24" @default.
- W2034954715 creator A5004837650 @default.
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- W2034954715 date "2014-02-01" @default.
- W2034954715 modified "2023-10-14" @default.
- W2034954715 title "Achievable angles between two compressed sparse vectors under RIP-induced norm/distance constraints" @default.
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- W2034954715 doi "https://doi.org/10.1109/iccnc.2014.6785390" @default.
- W2034954715 hasPublicationYear "2014" @default.
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