  Coupled tensor approximation has recently emerged as a promising approach for
the fusion of hyperspectral and multispectral images, reconciling state of the
art performance with strong theoretical guarantees. However, tensor-based
approaches previously proposed assume that the different observed images are
acquired under exactly the same conditions. A recent work proposed to
accommodate inter-image spectral variability in the image fusion problem using
a matrix factorization-based formulation, but did not account for
spatially-localized variations. Moreover, it lacks theoretical guarantees and
has a high associated computational complexity. In this paper, we consider the
image fusion problem while accounting for both spatially and spectrally
localized changes in an additive model. We first study how the general
identifiability of the model is impacted by the presence of such changes. Then,
assuming that the high-resolution image and the variation factors admit a
Tucker decomposition, two new algorithms are proposed -- one purely algebraic,
and another based on an optimization procedure. Theoretical guarantees for the
exact recovery of the high-resolution image are provided for both algorithms.
Experimental results show that the proposed method outperforms state-of-the-art
methods in the presence of spectral and spatial variations between the images,
at a smaller computational cost.
