Journal
IEEE TRANSACTIONS ON SIGNAL PROCESSING
Volume 58, Issue 7, Pages 3436-3447Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2010.2046897
Keywords
Adaptive algorithms; compressive sampling; coordinate descent; RLS; sparse linear regression
Categories
Funding
- NSF [CCF 0830480, CON 0824007]
- U.S. Army Research Laboratory [DAAD19-01-2-0011]
- Division of Computing and Communication Foundations
- Direct For Computer & Info Scie & Enginr [0830480] Funding Source: National Science Foundation
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Using the l(1)-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 l(1)-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.
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