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Constrained Cramér–Rao bounds for reconstruction problems formulated as coupled canonical polyadic decompositions

Abstract : We propose a theoretical performance analysis for a class of reconstruction problems, formulated as coupled canonical polyadic decompositions of two low-resolution tensor observations. We study a particular case when all the modes of the tensors are coupled. Unlike the case of a single coupling constraint, a fully-coupled model requires nonlinear constraints in some estimation scenarios. Thus we introduce two probabilistic scenarios. For each scenario, we derive the constrained Cramér-Rao bounds for the parameters and for the mean-squared error of the reconstructed tensor. We show that with a carefully chosen initialization, the maximum likelihood estimators reach the bounds, even in challenging cases (low signal-to-noise ratio or large tensor rank).
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https://hal.archives-ouvertes.fr/hal-03651874
Contributor : David Brie Connect in order to contact the contributor
Submitted on : Tuesday, April 26, 2022 - 10:17:37 AM
Last modification on : Monday, May 2, 2022 - 4:14:44 PM

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Clémence Prévost, Konstantin Usevich, Martin Haardt, Pierre Comon, David Brie. Constrained Cramér–Rao bounds for reconstruction problems formulated as coupled canonical polyadic decompositions. Signal Processing, Elsevier, 2022, 198, pp.108573. ⟨10.1016/j.sigpro.2022.108573⟩. ⟨hal-03651874⟩

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