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

Yannis Bekri (), Anatoli Juditsky () and Arkadi Nemirovski ()
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Yannis Bekri: LJK, Université Grenoble Alpes
Anatoli Juditsky: LJK, Université Grenoble Alpes
Arkadi Nemirovski: Georgia Institute of Technology

Journal of Optimization Theory and Applications, 2025, vol. 205, issue 3, No 14, 23 pages

Abstract: 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.

Keywords: Statistical linear inverse problems; Robust estimation; Observation matrix uncertainty; 62G05; 62G10; 90C90 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02666-9

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