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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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 60; no. 5; pp. 2194 - 2207
Main Authors: Dumitrescu, B., Onose, A., Helin, P., Tabus, I.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.05.2012
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
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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Summary: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.
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2012.2187285