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Designing Incoherent Frames Through Convex Techniques for Optimized Compressed Sensing

Rusu, Cristian and González-Prelcic, Nuria (2016) Designing Incoherent Frames Through Convex Techniques for Optimized Compressed Sensing. IEEE Transactions on Signal Processing, 64 (9). pp. 2334-2344. ISSN 1941-0476

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Abstract

The construction of highly incoherent frames, sequences of vectors placed on the unit hyper sphere of a finite dimensional Hilbert space with low correlation between them, has proven very difficult. Algorithms proposed in the past have focused on minimizing the absolute value off-diagonal entries of the Gram matrix of these structures. Recently, a method based on convex optimization that operates directly on the vectors of the frame has been shown to produce promising results. This paper gives a detailed analysis of the optimization problem at the heart of this approach and, based on these insights, proposes a new method that substantially outperforms the initial approach and all current methods in the literature for all types of frames, with low and high redundancy. We give extensive experimental results that show the effectiveness of the proposed method and its application to optimized compressed sensing.

Item Type: Article
Subjects: Q Science > QA Mathematics > Electronic computers. Computer science
T Technology > T Technology (General) > Information Technology > Electronic computers. Computer science

Q Science > QA Mathematics > Computer software
T Technology > T Technology (General) > Information Technology > Computer software
Divisions: School of Computing > Staff Research and Publications
Depositing User: CAOIMHE NI MHAICIN
Date Deposited: 02 Jul 2018 12:51
Last Modified: 02 Jul 2018 12:51
URI: http://trap.ncirl.ie/id/eprint/3036

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