Unsupervised coefficient learning framework for variational pansharpening

Pansharpening combines a panchromatic (PAN) image and a low-resolution multispectral (LRMS) image to generate a high-resolution multispectral (HRMS) image. Variational optimization (VO) approaches have garnered significant attention due to their data-independent generalization capabilities and robust performance. However, these methods often face challenges in accurately estimating coefficients, a critical factor influencing the quality of the final results. Existing VO approaches typically perform linear coefficient estimation at a reduced-resolution scale, which limits their effectiveness and adaptability. To address these limitations, we propose a novel VO-based method under an unsupervised coefficient learning (UCL) framework. This approach retains the generalization ability of VO while enabling precise coefficient estimation through a nonlinear, full-resolution learning technique. Furthermore, the UCL framework eliminates the need for additional training data beyond the input pair (i.e., a PAN image and a LRMS image), offering a flexible and extensible solution applicable to other traditional methods based on coefficient estimation. Qualitative and quantitative experimental assessments on reduced- and full-resolution datasets demonstrate that the proposed method achieves state-of-the-art performance. The code is available at https://github.com/Jin-liangXiao/UCL.