Adaptive signal processing algorithms: stability and performance
Adaptive signal processing algorithms: stability and performance
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Convergence of a block coordinate descent method for nondifferentiable minimization
Journal of Optimization Theory and Applications
Sparse LMS for system identification
ICASSP '09 Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing
RLS-weighted Lasso for adaptive estimation of sparse signals
ICASSP '09 Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing
Low-Complexity RLS Algorithms Using Dichotomous Coordinate Descent Iterations
IEEE Transactions on Signal Processing - Part II
IEEE Transactions on Signal Processing
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
IEEE Transactions on Information Theory
Compressive system identification: Sequential methods and entropy bounds
Digital Signal Processing
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Using the l1-norm to regularize the least-squares criterion, 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 high complexity, increasing memory requirements, and lack of tracking capability that batch Lasso estimators face when processing observations sequentially, the present paper develops a novel time-weighted Lasso (TWL) approach. Performance analysis reveals that TWL cannot estimate consistently the desired signal support without compromising rate of convergence. This motivates the development of a time- and norm-weighted Lasso (TNWL) scheme with l1-norm weights obtained from the recursive least-squares (RLS) algorithm. The resultant algorithm consistently estimates the support of sparse signals without reducing the convergence rate. To cope with sparsity-aware recursive real-time processing, novel adaptive algorithms are also developed to enable online coordinate descent solvers of TWL and TNWL that provably converge to the true sparse signal in the time-invariant case. Simulated tests compare competing alternatives and corroborate the performance of the novel algorithms in estimating time-invariant signals, and tracking time-varying signals under sparsity constraints.