Compressed sensing of time-varying signals
DSP'09 Proceedings of the 16th international conference on Digital Signal Processing
An adaptive greedy algorithm with application to nonlinear communications
IEEE Transactions on Signal Processing
Lasso-Kalman smoother for tracking sparse signals
Asilomar'09 Proceedings of the 43rd Asilomar conference on Signals, systems and computers
SPARLS: the sparse RLS algorithm
IEEE Transactions on Signal Processing
LS-CS-residual (LS-CS): compressive sensing on least squares residual
IEEE Transactions on Signal Processing
Online adaptive estimation of sparse signals: where RLS meets the l1-norm
IEEE Transactions on Signal Processing
Modified-CS: modifying compressive sensing for problems with partially known support
IEEE Transactions on Signal Processing
Adaptive algorithms for sparse system identification
Signal Processing
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The batch least-absolute shrinkage and selection operator (Lasso) has well-documented merits for estimating sparse signals of interest emerging in various applications, where observations adhere to parsimonious linear regression models. To cope with linearly growing complexity and memory requirements that batch Lasso estimators face when processing observations sequentially, the present paper develops a recursive Lasso algorithm that can also track slowly-varying sparse signals of interest. Performance analysis reveals that recursive Lasso can either estimate consistently the sparse signal's support or its nonzero entries, but not both. This motivates the development of a weighted version of the recursive Lasso scheme with weights obtained from the recursive least-squares (RLS) algorithm. The resultant RLS-weighted Lasso algorithm provably estimates sparse signals consistently. Simulated tests compare competing alternatives and corroborate the performance of the novel algorithms in estimating time-invariant and tracking slow-varying signals under sparsity constraints.