Performance bounds for coupled CP model in the framework of hyperspectral super-resolution

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

1 CRAN - Centre de Recherche en Automatique de Nancy
2 GIPSA-lab - Grenoble Images Parole Signal Automatique
3 Ilmenau University of Technology

We derive the constrained Cramér-Rao bounds for a coupled CP model with linear constraints applied to the hyperspectral super-resolution problem. For this problem, we consider two tensors representing low-resolution hyperspectral and mul-tispectral images. In a practical measurement setup, white Gaussian noise sequences are added to each tensor with different variances. The coupling constraints are expressed between the factor matrices of the canonical polyadic model for each tensor. We show that the estimator given by the coupled alternating least squares algorithm achieves the bounds for given Signal-to-Noise Ratios, but requires the knowledge of the ratio of variances of the additive Gaussian noise sequences on each tensor.

Mots clés: Data fusion; Cramér-Rao bounds; coupled decompositions; multimodal data; hyperspectral super-resolution

Domaines: Traitement du signal et de l'image [eess.SP]

Clémence Prevost, Konstantin Usevich, Pierre Comon, Martin Haardt, David Brie. Performance bounds for coupled CP model in the framework of hyperspectral super-resolution. 8th Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2019, Dec 2019, Le Gosier, Guadeloupe, France. ⟨hal-02303132v1⟩