SPARLS: The Sparse RLS Algorithm

We develop a recursive L 1 -regularized least squares (SPARLS) algorithm for the estimation of a sparse tap-weight vector in the adaptive filtering setting. The SPARLS algorithm exploits noisy observations of the tap-weight vector output stream and produces its estimate using an expectation-maximiza...

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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 58; no. 8; pp. 4013 - 4025
Main Authors: Babadi, B, Kalouptsidis, N, Tarokh, V
Format: Journal Article
Language:English
Published: New York IEEE 01.08.2010
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Adaptive filters
Algorithm design and analysis
Algorithms
Channels
compressed sensing
Computer simulation
Convergence
Error analysis
Filtering algorithms
Least squares approximation
Least squares method
Mathematical analysis
Recursive
Recursive estimation
Resonance light scattering
sparse system identification
State estimation
Steady-state
Vectors (mathematics)
Working environment noise
ISSN:1053-587X, 1941-0476
Online Access:Get full text
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Summary:We develop a recursive L 1 -regularized least squares (SPARLS) algorithm for the estimation of a sparse tap-weight vector in the adaptive filtering setting. The SPARLS algorithm exploits noisy observations of the tap-weight vector output stream and produces its estimate using an expectation-maximization type algorithm. We prove the convergence of the SPARLS algorithm to a near-optimal estimate in a stationary environment and present analytical results for the steady state error. Simulation studies in the context of channel estimation, employing multipath wireless channels, show that the SPARLS algorithm has significant improvement over the conventional widely used recursive least squares (RLS) algorithm in terms of mean squared error (MSE). Moreover, these simulation studies suggest that the SPARLS algorithm (with slight modifications) can operate with lower computational requirements than the RLS algorithm, when applied to tap-weight vectors with fixed support.
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2010.2048103