Title :
Sparse linear representation
Author :
Jeong, Halyun ; Kim, Young-Han
Author_Institution :
Dept. of ECE, UCSD, La Jolla, CA, USA
fDate :
June 28 2009-July 3 2009
Abstract :
This paper studies the question of how well a signal can be represented by a sparse linear combination of reference signals from an over complete dictionary. When the dictionary size is exponential in the dimension of signal, then the exact characterization of the optimal distortion is given as a function of the dictionary size exponent and the number of reference signals for the linear representation. Roughly speaking, every signal is sparse if the dictionary size is exponentially large, no matter how small the exponent is. Furthermore, an iterative method similar to matching pursuit that successively finds the best reference signal at each stage gives asymptotically optimal representations. This method is essentially equivalent to successive refinement for multiple descriptions and provides a simple alternative proof of the successive refinability of white Gaussian sources.
Keywords :
distortion; iterative methods; signal representation; sparse matrices; dictionary size exponent; iterative method; matching pursuit; optimal distortion; signal represention; sparse linear combination; sparse linear representation; white Gaussian sources; Dictionaries; Iterative methods; Linear approximation; Matching pursuit algorithms; Rate distortion theory;
Conference_Titel :
Information Theory, 2009. ISIT 2009. IEEE International Symposium on
Conference_Location :
Seoul
Print_ISBN :
978-1-4244-4312-3
Electronic_ISBN :
978-1-4244-4313-0
DOI :
10.1109/ISIT.2009.5205585