Sparse Solutions to Structured Underdetermined Systems in the Presence of Small Noise
Takos, Georgios
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https://hdl.handle.net/2142/81044
Description
Title
Sparse Solutions to Structured Underdetermined Systems in the Presence of Small Noise
Author(s)
Takos, Georgios
Issue Date
2007
Doctoral Committee Chair(s)
Christoforos N. Hadjicostis
Department of Study
Electrical and Computer Engineering
Discipline
Electrical and Computer Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Electronics and Electrical
Language
eng
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.
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