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Algorithms for the construction of incoherent frames under various design constraints

Rusu, Cristian, González-Prelcic, Nuria and Heath, Robert W. (2018) Algorithms for the construction of incoherent frames under various design constraints. Signal Processing, 152. pp. 363-372. ISSN 0165-1684

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Unit norm finite frames are generalizations of orthonormal bases with many applications in signal processing. An important property of a frame is its coherence, a measure of how close any two vectors of the frame are to each other. Low coherence frames are useful in compressed sensing applications. When used as measurement matrices, they successfully recover highly sparse solutions to linear inverse problems. This paper describes algorithms for the design of various low coherence frame types: real, complex, unital (constant magnitude) complex, sparse real and complex, nonnegative real and complex, and harmonic (selection of rows from Fourier matrices). The proposed methods are based on solving a sequence of convex optimization problems that update each vector of the frame. This update reduces the coherence with the other frame vectors, while other constraints on its entries are also imposed. Numerical experiments show the effectiveness of the methods compared to the Welch bound, as well as other competing algorithms, in compressed sensing applications.

Item Type: Article
Subjects: Q Science > QA Mathematics > Electronic computers. Computer science
T Technology > T Technology (General) > Information Technology > Electronic computers. Computer science
Divisions: School of Computing > Staff Research and Publications
Depositing User: Caoimhe Ní Mhaicín
Date Deposited: 13 Nov 2018 16:26
Last Modified: 13 Nov 2018 16:26

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