Title :
Subset selection in noise based on diversity measure minimization
Author :
Rao, Bhaskar D. ; Engan, Kjersti ; Cotter, Shane F. ; Palmer, Jason ; Kreutz-Delgado, Kenneth
Author_Institution :
Dept. of Electr. & Comput. Eng., California Univ., San Diego, La Jolla, CA, USA
fDate :
3/1/2003 12:00:00 AM
Abstract :
We develop robust methods for subset selection based on the minimization of diversity measures. A Bayesian framework is used to account for noise in the data and a maximum a posteriori (MAP) estimation procedure leads to an iterative procedure which is a regularized version of the focal underdetermined system solver (FOCUSS) algorithm. The convergence of the regularized FOCUSS algorithm is established and it is shown that the stable fixed points of the algorithm are sparse. We investigate three different criteria for choosing the regularization parameter: quality of fit; sparsity criterion; L-curve. The L-curve method, as applied to the problem of subset selection, is found not to be robust, and we propose a novel modified L-curve procedure that solves this problem. Each of the regularized FOCUSS algorithms is evaluated through simulation of a detection problem, and the results are compared with those obtained using a sequential forward selection algorithm termed orthogonal matching pursuit (OMP). In each case, the regularized FOCUSS algorithm is shown to be superior to the OMP in noisy environments.
Keywords :
Bayes methods; iterative methods; maximum likelihood estimation; minimisation; random noise; set theory; signal processing; Bayesian framework; L-curve method; MAP estimation; SNR; detection problem; diversity measure minimization; focal underdetermined system solver algorithm; iterative procedure; maximum a posteriori estimation; orthogonal matching pursuit; quality of fit; regularization parameter; sequential forward selection algorithm; signal-to-noise ratio; sparsity criterion; subset selection; Bayesian methods; Dictionaries; Iterative algorithms; Matching pursuit algorithms; Minimization methods; Noise measurement; Noise robustness; Pursuit algorithms; Signal to noise ratio; Working environment noise;
Journal_Title :
Signal Processing, IEEE Transactions on
DOI :
10.1109/TSP.2002.808076