Robust compressed sensing with bounded and structured uncertainties

Xiangyun Qing; Guosheng Hu; Xingyu Wang

Robust compressed sensing with bounded and structured uncertainties

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Author(s): Xiangyun Qing ^{1, 2} ; Guosheng Hu ³ ; Xingyu Wang ^{1, 2}
- Affiliations: 1: Key Laboratory of Advanced Control and Optimization for Chemical Processes, Ministry of Education, Shanghai, People's Republic of China;
  2: Department of Automation, East China University of Science and Technology, Shanghai, People's Republic of China;
  3: Centre for Vision, Speech and Signal Processing, University of Surrey, Guildford, UK
Source: Volume 8, Issue 7, September 2014, p. 783 – 791
DOI: 10.1049/iet-spr.2013.0260 , Print ISSN 1751-9675, Online ISSN 1751-9683

Received 30/06/2013, Accepted 28/02/2014, Revised 16/01/2014, Published 21/05/2014

The robust compressed sensing problem subject to a bounded and structured perturbation in the sensing matrix is solved in two steps. The alternating direction method of multipliers (ADMM) is first applied to obtain a robust support set. Unlike the existing robust signal recovery solutions, the proposed optimisation problem is convex. The ADMM algorithm that every subproblem has a global minimum is employed to solve the optimisation problem. Then, the standard robust regularised least-squares problem restrained to the support is solved to reduce the recovery error. The numerical tests show that the proposed approach provides a robust estimation of support set, although it is conservative to recover signal magnitudes as a result of minimising the worst-cast data error across all bounded perturbations.

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Robust compressed sensing with bounded and structured uncertainties

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