Hyperspectral and Multispectral Image Fusion Based on Low Rank Constrained Gaussian Mixture Model

This paper attempts to fuse a multispectral image and an auxiliary hyperspectral image (HSI) with no requirement of image registration. Most previous studies solve this problem with sparsity-based methods. However, in this paper, a novel fusion framework is developed based on a Gaussian mixture model (GMM): First, the GMM is adopted to extract the spectral information from the input HSI. Low-rank constraints are imposed on the covariance matrices of the model to solve the computational problem in the expectation-maximization approach. Second, considering the spatial self-similarity, a structure-similarity regularization term is designed to further enhance the quality of the reconstructed image. To that end, a forward–backward splitting method is adopted to cut down the computational complexity of the optimization. The proposed method does not require two well-aligned images, thus, it will not be influenced by the registration errors between two fusing images. Experimental results of a simulated data set and an actual satellite (EO-1/Hyperion/ALI) data set show that the proposed method displays a stable performance and outperforms many state-of-the-art methods with acceptable computational complexity, when registration errors are taken into consideration.