Pansharpening involves the spatial super-resolution of a low-resolution multispectral (LR-MS) image by leveraging a simultaneously acquired panchromatic (PAN) image, aiming to generate a high-resolution multispectral (HR-MS) image. Such an inverse problem mainly requires more accurately establishing the relation between the underlying HR-MS image and the PAN image. Because of the high redundancy of framelet transform, the framelet-based sparse error reconstruction has recently been well-investigated and achieved promising results. Nevertheless, previous works ignore the negative impact of the low-pass filter within the framelet, which experimentally distinguishes the coefficient similarity and reduces the error sparsity, thereby leading to limited numerical performance and high hyperparameter sensitivity. In this paper, we propose an improved pansharpening model via semi-framelet-guided sparse reconstruction, called SemiFGSR. This model only considers the partial rather than the whole framelet transform, which avoids the interference of low-frequency information, thus facilitating sparse reconstruction. To solve the proposed norm-based model, we develop an efficient proximal alternating minimization (PAM)-based algorithm and theoretically prove its convergence. Numerical experiments conducted on various datasets demonstrate the superiority of the SemiFGSR, revealing the effectiveness of such semi-framelet-guided improvement.

中文翻译：

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通过半框架引导的稀疏重建进行全色锐化

全色锐化涉及通过利用同时采集的全色（PAN）图像对低分辨率多光谱（LR-MS）图像进行空间超分辨率，旨在生成高分辨率多光谱（HR-MS）图像。这样的反问题主要需要更准确地建立底层HR-MS图像和PAN图像之间的关系。由于小框架变换的高冗余性，基于小框架的稀疏误差重构最近得到了深​​入研究并取得了可喜的结果。然而，以前的工作忽略了框架内低通滤波器的负面影响，它通过实验区分系数相似性并降低误差稀疏性，从而导致有限的数值性能和高超参数灵敏度。在本文中，我们提出了一种通过半框架引导稀疏重建改进的全色锐化模型，称为 SemiFGSR。该模型只考虑部分而不是整体的小框架变换，避免了低频信息的干扰，从而有利于稀疏重建。为了解决所提出的基于范数的模型，我们开发了一种高效的基于近端交替最小化（PAM）的算法，并从理论上证明了其收敛性。在各种数据集上进行的数值实验证明了 SemiFGSR 的优越性，揭示了这种半框架引导改进的有效性。