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Robust Signal Recovery Under Uncertain-but-Bounded Perturbations in Observation Matrix

Author

Listed:
  • Yannis Bekri

    (LJK, Université Grenoble Alpes)

  • Anatoli Juditsky

    (LJK, Université Grenoble Alpes)

  • Arkadi Nemirovski

    (Georgia Institute of Technology)

Abstract

In this paper our focus is on analysis and design of linear and polyhedral signal recoveries robust with respect to the deterministic uncertainty in the observation matrix. This can be seen as a “deterministic counterpart” of the work [1] where the case of random uncertainty was studied. We investigate the performance of estimates robust w.r.t. deterministic norm-bounded matrix uncertainty, derive efficiently computable bounds for the estimation risk and discuss the construction of “presumably good” estimates.

Suggested Citation

  • Yannis Bekri & Anatoli Juditsky & Arkadi Nemirovski, 2025. "Robust Signal Recovery Under Uncertain-but-Bounded Perturbations in Observation Matrix," Journal of Optimization Theory and Applications, Springer, vol. 205(3), pages 1-23, June.
    • Handle: RePEc:spr:joptap:v:205:y:2025:i:3:d:10.1007_s10957-025-02666-9
    DOI: 10.1007/s10957-025-02666-9
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    References listed on IDEAS

    as
    1. Tempo, R. & Vicino, A., 1990. "Optimal algorithms for system identification: a review of some recent results," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 585-595.
    2. Aharon Ben-Tal & Arkadi Nemirovski & Cornelis Roos, 2003. "Extended Matrix Cube Theorems with Applications to (mu)-Theory in Control," Mathematics of Operations Research, INFORMS, vol. 28(3), pages 497-523, August.
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