Sparsity-cognizant total least-squares for perturbed compressive sampling

Hao Zhu, Geert Leus, Georgios B Giannakis

Research output: Contribution to journalArticlepeer-review

266 Scopus citations

Abstract

Solving linear regression problems based on the total least-squares (TLS) criterion has well-documented merits in various applications, where perturbations appear both in the data vector as well as in the regression matrix. However, existing TLS approaches do not account for sparsity possibly present in the unknown vector of regression coefficients. On the other hand, sparsity is the key attribute exploited by modern compressive sampling and variable selection approaches to linear regression, which include noise in the data, but do not account for perturbations in the regression matrix. The present paper fills this gap by formulating and solving (regularized) TLS optimization problems under sparsity constraints. Near-optimum and reduced-complexity suboptimum sparse (S-) TLS algorithms are developed to address the perturbed compressive sampling (and the related dictionary learning) challenge, when there is a mismatch between the true and adopted bases over which the unknown vector is sparse. The novel S-TLS schemes also allow for perturbations in the regression matrix of the least-absolute selection and shrinkage selection operator (Lasso), and endow TLS approaches with ability to cope with sparse, under-determined errors-in-variables models. Interesting generalizations can further exploit prior knowledge on the perturbations to obtain novel weighted and structured S-TLS solvers. Analysis and simulations demonstrate the practical impact of S-TLS in calibrating the mismatch effects of contemporary grid-based approaches to cognitive radio sensing, and robust direction-of-arrival estimation using antenna arrays.

Original languageEnglish (US)
Article number5706373
Pages (from-to)2002-2016
Number of pages15
JournalIEEE Transactions on Signal Processing
Volume59
Issue number5
DOIs
StatePublished - May 1 2011

Keywords

  • Direction-of-arrival estimation
  • errors-in-variables models
  • sparsity
  • spectrum sensing
  • total least-squares

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