Title :
Efficient backward elimination algorithm for sparse signal representation using overcomplete dictionaries
Author :
Cotter, Shane F. ; Kreutz-Delgado, K. ; Rao, B.D.
Author_Institution :
Dept. of Electr. & Comput. Eng., California Univ., San Diego, La Jolla, CA, USA
fDate :
5/1/2002 12:00:00 AM
Abstract :
A sparse representation of a signal, i.e., a representation using a small number of vectors chosen from a dictionary of vectors, is highly desirable in many applications. Here, we extend the backward elimination sparse representation algorithm presented by Reeves (see ibid., vol.6, p.266-68, Oct. 1999) to allow for an overcomplete dictionary and develop recursions for its implementation. In the overcomplete case, the representation error cannot be used as a general criterion for elimination of a dictionary vector and other criteria must be considered. Simulation on a test-case dictionary shows that the performance of the proposed algorithm can improve upon that of forward selection methods.
Keywords :
inverse problems; matrix algebra; signal representation; backward elimination sparse representation algorithm; efficient backward elimination algorithm; forward selection methods; linear inverse problem; matrix; overcomplete dictionaries; representation error; simulation; sparse signal representation; vectors dictionary; Computer errors; Dictionaries; Greedy algorithms; Inverse problems; Minimization methods; Signal processing; Signal processing algorithms; Signal representations; Testing; Vectors;
Journal_Title :
Signal Processing Letters, IEEE
DOI :
10.1109/LSP.2002.1009004