  This paper presents a multi-band image fusion algorithm based on unsupervised
spectral unmixing for combining a high-spatial low-spectral resolution image
and a low-spatial high-spectral resolution image. The widely used linear
observation model (with additive Gaussian noise) is combined with the linear
spectral mixture model to form the likelihoods of the observations. The
non-negativity and sum-to-one constraints resulting from the intrinsic physical
properties of the abundances are introduced as prior information to regularize
this ill-posed problem. The joint fusion and unmixing problem is then
formulated as maximizing the joint posterior distribution with respect to the
endmember signatures and abundance maps, This optimization problem is attacked
with an alternating optimization strategy. The two resulting sub-problems are
convex and are solved efficiently using the alternating direction method of
multipliers. Experiments are conducted for both synthetic and semi-real data.
Simulation results show that the proposed unmixing based fusion scheme improves
both the abundance and endmember estimation comparing with the state-of-the-art
joint fusion and unmixing algorithms.
