From sparse signals to sparse residuals for robust sensing

Vasileios Kekatos, Georgios B Giannakis

Research output: Contribution to journalArticlepeer-review

41 Scopus citations


One of the key challenges in sensor networks is the extraction of information by fusing data from a multitude of distinct, but possibly unreliable sensors. Recovering information from the maximum number of dependable sensors while specifying the unreliable ones is critical for robust sensing. This sensing task is formulated here as that of finding the maximum number of feasible subsystems of linear equations and proved to be NP-hard. Useful links are established with compressive sampling, which aims at recovering vectors that are sparse. In contrast, the signals here are not sparse, but give rise to sparse residuals. Capitalizing on this form of sparsity, four sensing schemes with complementary strengths are developed. The first scheme is a convex relaxation of the original problem expressed as a second-order cone program (SOCP). It is shown that when the involved sensing matrices are Gaussian and the reliable measurements are sufficiently many, the SOCP can recover the optimal solution with overwhelming probability. The second scheme is obtained by replacing the initial objective function with a concave one. The third and fourth schemes are tailored for noisy sensor data. The noisy case is cast as a combinatorial problem that is subsequently surrogated by a (weighted) SOCP. Interestingly, the derived cost functions fall into the framework of robust multivariate linear regression, while an efficient block-coordinate descent algorithm is developed for their minimization. The robust sensing capabilities of all schemes are verified by simulated tests.

Original languageEnglish (US)
Article number5746650
Pages (from-to)3355-3368
Number of pages14
JournalIEEE Transactions on Signal Processing
Issue number7
StatePublished - Jul 2011

Bibliographical note

Funding Information:
Manuscript received May 11, 2010; revised November 01, 2010 and March 27, 2011; accepted March 31, 2011. Date of publication April 11, 2011; date of current version June 15, 2011. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Jean-Yves Tourneret. This work was supported by the European Community’s Seventh Framework Programme (FP7/2008 under Grant 234914) and by NSF Grant CCF-1016605. Part of this work was presented at the Eleventh IEEE International Workshop on Signal Processing Advances in Wireless Communications, Marrakech, Morocco, June 2010.

Copyright 2011 Elsevier B.V., All rights reserved.


  • Compressive sampling
  • convex relaxation
  • coordinate descent
  • multivariate regression
  • robust methods
  • sensor networks

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