Online sparse system identification and signal reconstruction using projections onto weighted ℓ1 balls

Yannis Kopsinis, Konstantinos Slavakis, Sergios Theodoridis

Research output: Contribution to journalArticlepeer-review

116 Scopus citations


This paper presents a novel projection-based adaptive algorithm for sparse signal and system identification. The sequentially observed data are used to generate an equivalent sequence of closed convex sets, namely hyperslabs. Each hyperslab is the geometric equivalent of a cost criterion, that quantifies "data mismatch". Sparsity is imposed by the introduction of appropriately designed weighted ℓ1 balls and the related projection operator is also derived. The algorithm develops around projections onto the sequence of the generated hyperslabs as well as the weighted ℓ1 balls. The resulting scheme exhibits linear dependence, with respect to the unknown system's order, on the number of multiplications/ additions and an Ο(Llog2L) dependence on sorting operations, where $L$ is the length of the system/signal to be estimated. Numerical results are also given to validate the performance of the proposed method against the Least-Absolute Shrinkage and Selection Operator (LASSO) algorithm and two very recently developed adaptive sparse schemes that fuse arguments from the LMS/RLS adaptation mechanisms with those imposed by the lasso rational.

Original languageEnglish (US)
Article number5621929
Pages (from-to)936-952
Number of pages17
JournalIEEE Transactions on Signal Processing
Issue number3
StatePublished - Mar 2011

Bibliographical note

Funding Information:
Manuscript received April 20, 2010; revised August 10, 2010; accepted October 12, 2010. Date of publication November 09, 2010; date of current version February 09, 2011. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Shengli Zhou. This work was supported in part by the RACTI Patras, Greece.


  • Sparsity
  • adaptive filtering
  • compressive sensing
  • projections


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