Hyperspectral pansharpening is a process of merging a high-resolution panchromatic (PAN) image and a low-resolution hyperspectral (LRHS) image to create a single high-resolution hyperspectral (HRHS) image. Existing Bayesian-based HS pansharpening methods require designing handcraft image prior to characterize the image features, and deep learning-based HS pansharpening methods usually require a large number of paired training data and suffer from poor generalization ability. To address these issues, in this work, we propose a low-rank diffusion model for hyperspectral pansharpening by simultaneously leveraging the power of the pre-trained deep diffusion model and better generalization ability of Bayesian methods. Specifically, we assume that the HRHS image can be recovered from the product of two low-rank tensors, i.e., the base tensor and the coefficient matrix. The base tensor lies on the image field and has a low spectral dimension. Thus, we can conveniently utilize a pre-trained remote sensing diffusion model to capture its image structures. Additionally, we derive a simple yet quite effective way to pre-estimate the coefficient matrix from the observed LRHS image, which preserves the spectral information of the HRHS. Experimental results demonstrate that the proposed method performs better than some popular traditional approaches and gains better generalization ability than some DL-based methods. The code is released in https://github.com/xyrui/PLRDiff.
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