  The hyperspectral image (HSI) unmixing task is essentially an inverse
problem, which is commonly solved by optimization algorithms under a predefined
(non-)linear mixture model. Although these optimization algorithms show
impressive performance, they are very computational demanding as they often
rely on an iterative updating scheme. Recently, the rise of neural networks has
inspired lots of learning based algorithms in unmixing literature. However,
most of them lack of interpretability and require a large training dataset. One
natural question then arises: can one leverage the model based algorithm and
learning based algorithm to achieve interpretable and fast algorithm for HSI
unmixing problem? In this paper, we propose two novel network architectures,
named U-ADMM-AENet and U-ADMM-BUNet, for abundance estimation and blind
unmixing respectively, by combining the conventional optimization-model based
unmixing method and the rising learning based unmixing method. We first
consider a linear mixture model with sparsity constraint, then we unfold
Alternating Direction Method of Multipliers (ADMM) algorithm to construct the
unmixing network structures. We also show that the unfolded structures can find
corresponding interpretations in machine learning literature, which further
demonstrates the effectiveness of proposed methods. Benefit from the
interpretation, the proposed networks can be initialized by incorporating prior
information about the HSI data. Different from traditional unfolding networks,
we propose a new training strategy for proposed networks to better fit in the
HSI applications. Extensive experiments show that the proposed methods can
achieve much faster convergence and competitive performance even with very
small size of training data, when compared with state-of-art algorithms.
