Pan-sharpening aims at acquiring a multispectral image with a high spatial resolution by fusing a low-resolution multispectral image and a panchromatic image. In order to improve spatial details and reduce spectral distortions, we develop a new pan-sharpening model based on the Bayesian theory, which involves three assumptions: 1) the low-resolution multispectral images are generally decimated from the high-resolution multispectral images by convolution with a blurring kernel; 2) different from

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... most pan-sharpening methods that use linear manners to preserve spatial information, we attempt a nonlinear manner based on a convolutional neural network composed of the proposed multiscale recursive blocks, and we train our network parameters in multiorder gradient domains to preserve more spatial structures; and 3) we introduce an anisotropic total variation prior in multiorder gradient domains to reconstruct better image edges and details. We establish the posterior probability model based on the above assumptions and derive an efficient optimization scheme to address the proposed objective function. Final experimental results demonstrate that the proposed model can overcome the restriction of a linear model and achieve better spectral and spatial fusion, compared with several traditional and deep-learning-based pan-sharpening approaches. In addition, our model achieves more promising generalization across different satellites than other deep-learning-based methods. Index Terms-Bayesian theory, convolutional neural network (CNN), multiorder gradient, pan-sharpening.