Nonnegative Block-Term Decomposition with the β-Divergence: Joint Data Fusion and Blind Spectral Unmixing

Abstract

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 superresolution image. The method, dubbed as β-(L r ,L r ,1)-NBTD, relies on three key elements: (1) the nonnegative decomposition in rank-(L r ,L r ,1) block-terms of the superresolution 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 lowrank block-term factors. We show on numerical experiments that β-(L r ,L r ,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.