Unsupervised Hyperspectral and Multispectral Images Fusion Based on Nonlinear Variational Probabilistic Generative Model

Due to hardware limitations, it is challenging for sensors to acquire images of high resolution in both spatial and spectral domains, which arouses a trend that utilizing a low-resolution hyperspectral image (LR-HSI) and a high-resolution multispectral image (HR-MSI) to fuse an HR-HSI in an unsupervised manner. Considering the fact that most existing methods are restricted by using linear spectral unmixing, we propose a nonlinear variational probabilistic generative model (NVPGM) for the unsupervised fusion task based on nonlinear unmixing. We model the joint full likelihood of the observed pixels in an LR-HSI and an HR-MSI, both of which are assumed to be generated from the corresponding latent representations, i.e., the abundance vectors. The sufficient statistics of the generative conditional distributions are nonlinear functions with respect to the latent variable, realized by neural networks, which results in a nonlinear spectral mixture model. For scalability and efficiency, we construct two recognition models to infer the latent representations, which are parameterized by neural networks as well. Simultaneously inferring the latent representations and optimizing the parameters are achieved using stochastic gradient variational inference, after which the target HR-HSI is retrieved via feedforward mapping. Though without supervised information about the HR-HSI, NVPGM still can be trained based on extra LR-HSI and HR-MSI data sets in advance unsupervisedly and processes the images at the test phase in real time. Three commonly used data sets are used to evaluate the effectiveness and efficiency of NVPGM, illustrating the outperformance of NVPGM in the unsupervised LR-HSI and HR-MSI fusion task.