NONNEGATIVE BLOCK-TERM DECOMPOSITION WITH THE β-DIVERGENCE: JOINT DATA FUSION AND BLIND SPECTRAL UNMIXING

Clémence Prévost (1) , Valentin Leplat (2)

1 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
2 Skoltech - Skolkovo Institute of Science and Technology [Moscow]

We present a new method for solving simultaneously two problems: (1) hyperspectral and multispectral image fusion, and (2) the blind spectral unmixing of the unknown super-resolution image. The method, dubbed as β-(Lr ,Lr ,1)-NBTD, relies on three key elements: (1) the nonnegative decomposition in rank-(Lr ,Lr ,1) block-terms of the super-resolution tensor, (2) the joint factorization of the input images, and (3) the formulation of a family of optimization problems including the β-divergences objective functions. In order to solve the two problems at hand, we propose multiplicative updates based on majorization-minimization. We come up with a family of simple, robust and efficient algorithms, adaptable to various noise statistics. As a byproduct, we propose a new robust initialization for the low-rank block-term factors. We show on numerical experiments that β-(Lr ,Lr ,1)-NBTD competes favorably with State-Of-The Arts methods for solving the super-resolution problem, while accurately solving the unmixing problem for various noise statistics.

Mots clés: Nonnegative tensor factorization; block-term decomposition; beta-divergence; blind spectral unmixing; hyperspectral super-resolution

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

Clémence Prévost, Valentin Leplat. NONNEGATIVE BLOCK-TERM DECOMPOSITION WITH THE β-DIVERGENCE: JOINT DATA FUSION AND BLIND SPECTRAL UNMIXING. 2022. ⟨hal-03831661⟩