Graph-Based Logarithmic Low-Rank Tensor Decomposition for the Fusion of Remotely Sensed Images

Hyperspectral images with high spatial resolution play an important role in material classification, change detection, and others. However, owing to the limitation of imaging sensors, it is difficult to directly acquire images with both high spatial resolution and high spectral resolution. Therefore, the fusion of remotely sensed images is an effective way to obtain high-resolution desired data, which is usually an ill-posed inverse problem and susceptible to noise corruption. To address these issues, a low-rank model based on tensor decomposition is proposed to fuse hyperspectral and multispectral images by incorporating graph regularization, in which the logarithmic low-rank function is utilized to suppress the small components for denoising. Furthermore, this article takes advantage of the local spatial similarity of remotely sensed images to enhance the reconstruction performance by constructing spatial graphs, and also promotes signature smoothing between adjacent endmember spectra using the neighborhood-based spectral graph regularization. Finally, a set of efficient solvers is carefully designed via alternating optimization for closed-from solutions and computational reduction, in which vector-matrix operators are adapted to solve the 3-D core tensor. Experimental tests on several real datasets illustrate that the proposed fusion method yields better reconstruction performance than the current state-of-the-art methods, and can significantly suppress noise at the same time.