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

Abstract

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 highresolution 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 paper 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 three-dimensional core tensor. Experimental tests on several real datasets illustrate that the proposed fusion method yields better reconstruction performance than the current stateof-the-art methods, and can significantly suppress noise at the same time.

A Review of Spatial Enhancement of Hyperspectral Remote Sensing Imaging Techniques

“…Prior information must be incorporated in order to regularize Equation 27. For instance, in [149], the authors take advantage of the similarities between adjacent bands as well as neighboring pixels, and impose graph regularization on spatial and spectral matrices separately to minimize the effects of distortion. Another example is demonstrated in [265], where Dian and Li propose a Low Tensor Multi-Rank (LTMR) regularization method that exploits high correlation among spectral bands, as well as non-local spatial similarities.…”

Piecewise Weighted Smoothing Regularization in Tight Framelet Domain for Hyperspectral Image Restoration

“…Recently, the widely-used tensor decomposition methods mainly include Tucker decomposition [19], tensor ring decomposition [20], BTD decomposition [21], Mode-3 decomposition [22] and so on. Ma et al [23] incorporated graph smoothing and low-rank regularization into the model of Tucker tensor decomposition. Chen [24] constructed a low-rank tensor decomposition model to capture global spatial-spectral correlation.…”