Deep bidirectional hierarchical matrix factorization model for hyperspectral unmixing

Existing deep nonnegative matrix factorization-based approaches treat shallow and deep layers equally or with similar strategies, neglecting the heterogeneous physical structures between the shallow and progressively deeper layers, thus failing to explore the latent different sub-manifold structures in the hyperspectral image. In this paper, we propose a deep nonnegative matrix factorization model with bidirectional constraints to achieve hyperspectral unmixing. The sub-manifold structures in hyperspectral image are fully exploited by filtering and penalizing the shallow abundance layer with a denoised regularizer and a manifold regularizer. In contrast to the shallow abundance layer, the remaining layers are constrained by an extremely common regularizer to avoid over-denoising and maintain fidelity. In this way, the fine cues between different substances are exploited to a large extent. Additionally, the overall reconstruction error can be well controlled because the performance of the designed feedback mechanism can be fine-tuned by the inverse hierarchical constraints. Finally, we employ Nesterov's optimal gradient method to solve the optimization problem effectively. Experiment results are conducted on both synthetic datasets and real datasets, and all results show that the proposed method is superior to recent canonical unmixing methods.