Sparse Solutions to Structured Underdetermined Systems in the Presence of Small Noise

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Electrical and Computer Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Takos, Georgios

Contributors dc:contributor

• Christoforos N. Hadjicostis

• Engineering, Electronics and Electrical

Language dc:language

eng

Identifier

(MiAaPQ)AAI3290396

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/81044