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Title:Sparse Solutions to Structured Underdetermined Systems in the Presence of Small Noise
Author(s):Takos, Georgios
Doctoral Committee Chair(s):Christoforos N. Hadjicostis
Department / Program:Electrical and Computer Engineering
Discipline:Electrical and Computer Engineering
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):Engineering, Electronics and Electrical
Abstract:In addition, we provide an upper bound on the magnitude of the small noise to guarantee the correct determination of the number of nonzero entries of our unknown sparse vector, as well as an upper bound on the magnitude of the small noise to guarantee the correct localization of these nonzero entries. Simulations suggest that the first bound is very tight and that the two proposed algorithms outperform existing analytical schemes in the literature. Furthermore, we prove, in the case of real-number DFT codes, that if a fixed number of bits is available for the representation of real numbers, then these bits must be allocated uniformly among the entries of the codeword to optimize performance. Finally, we generalize the types of matrices our recovery algorithms can handle in the presence of small noise.
Issue Date:2007
Description:128 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2007.
Other Identifier(s):(MiAaPQ)AAI3290396
Date Available in IDEALS:2015-09-25
Date Deposited:2007

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