Hyperspecral Unmixing Based on Multilinear Mixing Model Using Convolutional Autoencoders

Unsupervised spectral unmixing (SU) consists of representing each observed pixel as a combination of several pure materials known as endmembers, along with their corresponding abundance fractions. Beyond the linear assumption, various nonlinear unmixing models have been proposed, with the associated optimization problems solved either by traditional optimization algorithms or deep learning techniques. Current deep-learning-based nonlinear unmixing mainly focuses on additive, bilinear-based formulations. The multilinear mixing model (MLM) offers a unique perspective by interpreting the reflection process by discrete Markov chains, allowing it to account for the interactions between endmembers up to infinite order. However, explicitly simulating the physics of MLM using neural networks has remained a challenging problem. In this article, we propose a novel autoencoder (AE)-based network for unsupervised unmixing based on MLM. Leveraging an elaborate network design, this approach explicitly models the relationships among all model parameters: endmembers, abundances, and transition probability. The network operates in two modes: MLM-1DAE, which considers only pixelwise spectral information, and MLM-3DAE, which explores spectral-spatial correlations within input patches. Experiments on both the synthetic and real datasets validate the effectiveness of the proposed method, demonstrating competitive performance compared with classic MLM-based solutions. The code is available at https://github.com/ting-Fang09/Hyperspectral-unmixing-MLM-AE.