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Christoforos N. Hadjicostis Takos, Georgios 2015-09-25T20:09:23Z 2015-09-25T20:09:23Z 10000-01-01 2007 2007 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. Made available in DSpace on 2015-09-25T20:09:23Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3290396.pdf: 2753076 bytes, checksum: afb1f2b4a92261c8df4c5956b8e9fc36 (MD5) Previous issue date: 2007 Embargo set by: Seth Robbins for item 82326 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 128 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2007. http://hdl.handle.net/2142/81044 (MiAaPQ)AAI3290396 eng Engineering, Electronics and Electrical Sparse Solutions to Structured Underdetermined Systems in the Presence of Small Noise text Electrical and Computer Engineering Electrical and Computer Engineering University of Illinois at Urbana-Champaign Dissertation Ph.D.