Title :
Explicit matrices for sparse approximation
Author :
Khajehnejad, Amin ; Tehrani, Arash Saber ; Dimakis, Alexandros G. ; Hassibi, Babak
Author_Institution :
Dept. of Electr. Eng., California Inst. of Technol., Pasadena, CA, USA
fDate :
July 31 2011-Aug. 5 2011
Abstract :
We show that girth can be used to certify that sparse compressed sensing matrices have good sparse approximation guarantees. This allows us to present the first deterministic measurement matrix constructions that have an optimal number of measurements for ℓ1/ℓ1 approximation. Our techniques are coding theoretic and rely on a recent connection of compressed sensing to LP relaxations for channel decoding.
Keywords :
approximation theory; channel coding; decoding; sparse matrices; LP relaxations; channel decoding; explicit matrices; first deterministic measurement matrix constructions; sparse approximation; sparse compressed sensing matrices; Approximation methods; Compressed sensing; Decoding; Parity check codes; Sparse matrices; Symmetric matrices; USA Councils;
Conference_Titel :
Information Theory Proceedings (ISIT), 2011 IEEE International Symposium on
Conference_Location :
St. Petersburg
Print_ISBN :
978-1-4577-0596-0
Electronic_ISBN :
2157-8095
DOI :
10.1109/ISIT.2011.6034170
