Reduced complexity bounded error subset selection

A reduced complexity version of the bounded error subset selection (BESS) algorithm is proposed. By relaxing the integer constraint in the original BESS algorithm, we show that the BESS problem can be reformulated as an ordinary linear program instead of an integer program with exponential worst-case complexity. We retain the sparseness of the representation in the modified BESS by weighting the dictionary with the minimum 2-norm solution of the subset selection problem corresponding to the BESS problem at hand. The proposed algorithm is compared to the basis pursuit, orthogonal matching pursuit, and the best orthogonal basis algorithms. It is shown that the proposed algorithm has a better packing property and an improved rate-distortion behavior.

[1]  Ingrid Daubechies,et al.  Time-frequency localization operators: A geometric phase space approach , 1988, IEEE Trans. Inf. Theory.

[2]  Stéphane Mallat,et al.  Matching pursuits with time-frequency dictionaries , 1993, IEEE Trans. Signal Process..

[3]  Ahmed H. Tewfik,et al.  Bounded subset selection with noninteger coefficients , 2004, 2004 12th European Signal Processing Conference.

[4]  Ahmed H. Tewfik,et al.  A sparse solution to the bounded subset selection problem: a network flow model approach , 2004, 2004 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[5]  Michael A. Saunders,et al.  Atomic Decomposition by Basis Pursuit , 1998, SIAM J. Sci. Comput..

[6]  Y. C. Pati,et al.  Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition , 1993, Proceedings of 27th Asilomar Conference on Signals, Systems and Computers.

[7]  Balas K. Natarajan,et al.  Sparse Approximate Solutions to Linear Systems , 1995, SIAM J. Comput..

[8]  Ronald R. Coifman,et al.  Entropy-based algorithms for best basis selection , 1992, IEEE Trans. Inf. Theory.