Constrained Cramér-Rao lower bounds for CP-based hyperspectral super-resolution

Clémence Prévost (1) , Konstantin Usevich (1) , Martin Haardt (2) , Pierre Comon (3) , David Brie (1)

1 CRAN - Centre de Recherche en Automatique de Nancy
2 TU - Technische Universität Ilmenau
3 GIPSA-GAIA - GIPSA Pôle Géométrie, Apprentissage, Information et Algorithmes

We propose a theoretical performance analysis forthe hyperspectral super-resolution task, formulated as a coupledcanonical polyadic decomposition. We introduce two probabilisticscenarios along with different parameterizations, then deriveconstrained Cram ́er-Rao lower bounds (CCRB) for the proposedscenarios. We then illustrate the versatility of the CCRB through-out a set of experiments, including its usefulness to design thehyperspectral measurement system. We also assess the relativeperformance of existing estimators and use the CCRB as a toolto design more efficient algorithms.

Domaines: Traitement du signal et de l'image [eess.SP]; Applications [stat.AP]

Clémence Prévost, Konstantin Usevich, Martin Haardt, Pierre Comon, David Brie. Constrained Cramér-Rao lower bounds for CP-based hyperspectral super-resolution. 2020. ⟨hal-03083709⟩