Graph-Based Tensor Bayesian Multispectral Image Fusion With Nonconvex Tensor Rank Minimization Model

Multispectral (MS) image fusion refers to the fusion of the low-resolution MS (LRMS) image and the corresponding panchromatic (Pan) image of the same earth scenes, which aims to produce the high-resolution MS (HRMS) image and has been an important and popular research subject in remote sensing. Specifically, the MS image belongs to the 3-D data and has strong spatial-spectral structural correlations and spectral-band correlations, thus the MS image has the preferable tensor property, which can be more actually and suitably modeled as an order-3 tensor. To fully exploit the tensor-based properties of MS and the graph-based spectral-band correlations of MS, this article proposes a unified graph-based nonconvex tensor rank minimization (GNTRM) model for MS image fusion from the perspectives of Bayesian inference, tensor representation, and graph representation. Based on the tensor representation of MS, this article particularly exploits the tensor low-tubal-rank prior between HRMS and Pan and proposes an HRMS minus Pan-guided nonconvex tensor low-rank prior term. Moreover, based on the graph representation, this article further constructs an effective graph representation of MS to model the graph-based spectral-band correlations of MS and proposes an HRMS minus LRMS-guided graph regularization prior term. Therefore, the unified GNTRM model is constructed by combining the HRMS minus Pan-guided nonconvex tensor low-rank prior term, the HRMS minus LRMS-guided graph regularization prior term, and the spatial degradation-guided spectral fidelity constraint term between HRMS and LRMS. Furthermore, the proposed GNTRM model is optimized via the alternating direction method of multipliers (ADMMs). Moreover, the systematical experiments on reduced-resolution and full-resolution MS datasets demonstrate the superiority of GNTRM. The code is available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/pengfeiliu-90/GNTRM</uri>.