Greedy Sparse RLS

Starting from the orthogonal (greedy) least squares method, we build an adaptive algorithm for finding online sparse solutions to linear systems. The algorithm belongs to the exponentially windowed recursive least squares (RLS) family and maintains a partial orthogonal factorization with pivoting of...

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Vydáno v:	IEEE transactions on signal processing Ročník 60; číslo 5; s. 2194 - 2207
Hlavní autoři:	Dumitrescu, B., Onose, A., Helin, P., Tabus, I.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York, NY IEEE 01.05.2012 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	Adaptive algorithms Algorithms Applied sciences Approximation algorithms audio coding channel identification Channels Coding, codes Computation Construction Criteria Detection, estimation, filtering, equalization, prediction Exact sciences and technology Factorization Information theory Information, signal and communications theory Least squares approximation Least squares method Matching pursuit algorithms Mathematical models Miscellaneous orthogonal least squares Signal and communications theory Signal processing Signal processing algorithms Signal, noise sparse filters Studies Telecommunications and information theory Vectors channel identification Time variable channel Lossless circuit Audio signal processing Adaptive algorithm Adaptive algorithms Acoustic signal processing Recursive algorithm Factorization Linear prediction Audio coding Linear system Simulation sparse filters Least squares method On line processing orthogonal least squares Greedy algorithm Recursive method Signal processing Least mean squares methods Information theory
ISSN:	1053-587X, 1941-0476
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Popis
Shrnutí:	Starting from the orthogonal (greedy) least squares method, we build an adaptive algorithm for finding online sparse solutions to linear systems. The algorithm belongs to the exponentially windowed recursive least squares (RLS) family and maintains a partial orthogonal factorization with pivoting of the system matrix. For complexity reasons, the permutations that bring the relevant columns into the first positions are restrained mainly to interchanges between neighbors at each time moment. The storage scheme allows the computation of the exact factorization, implicitly working on indefinitely long vectors. The sparsity level of the solution, i.e., the number of nonzero elements, is estimated using information theoretic criteria, in particular Bayesian information criterion (BIC) and predictive least squares. We present simulations showing that, for identifying sparse time-varying FIR channels, our algorithm is consistently better than previous sparse RLS methods based on the -norm regularization of the RLS criterion. We also use our sparse greedy RLS algorithm for computing linear predictions in a lossless audio coding scheme and obtain better compression than MPEG4 ALS using an RLS-LMS cascade.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 ObjectType-Article-2 ObjectType-Feature-1 content type line 23
ISSN:	1053-587X 1941-0476
DOI:	10.1109/TSP.2012.2187285