In this article, we propose a variational approach for fusion of two coregistered high-resolution panchromatic (HRP) and low-resolution multispectral (LRM) images to reach the high-resolution multispectral (HRM) one, i.e., pan-sharpening. In this fusion technique, there is a tradeoff between structural information of an HRP image and spectral information of LRM one. To reconstruct the HRM image, which benefits from the best characteristics of both images, we consider several fidelity terms. The structural fidelity term is used to transfer structural information of an HRP image to HRM one, and a spectral fidelity term is utilized to preserve spectral consistency between HRM and LRM images throughout the fusion process. To reduce the spectral distortion occurred due to the discrepancy between intensity values of HRP and LRM images, a novel spatial–spectral fidelity term is designed to keep the intensity ratio between multispectral and panchromatic pixels in the high-resolution space as the same as the low-resolution space. Moreover, the total variation (TV) regularization term is employed as a prior to promote the sparseness of gradient in HRM bands. These fidelity terms were formulated in a convex optimization problem. However, the structural and TV terms made this optimization problem nondifferentiable. Therefore, we developed an efficient majorization–minimization algorithm for solving the optimization problem. The proposed method applied to three datasets, acquired by WorldView-3, Deimos-2, and QuickBird satellites. To assess the effectiveness of the proposed method, visual analysis, as well as quantitative comparison to various pan-sharpening methods, was carried out. The experimental results suggested that the proposed method outperformed the competitors visually and quantitatively.

中文翻译：

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使用新的空间光谱一致性项融合全色和多光谱图像的变分方法

在本文中，我们提出了一种融合两个共同配准的高分辨率全色 (HRP) 和低分辨率多光谱 (LRM) 图像以达到高分辨率多光谱 (HRM) 图像的变分方法，即全色锐化。在这种融合技术中，HRP 图像的结构信息和 LRM 图像的光谱信息之间存在权衡。为了重建受益于两幅图像最佳特征的 HRM 图像，我们考虑了几个保真度项。结构保真项用于将 HRP 图像的结构信息传输到 HRM 图像，光谱保真项用于在整个融合过程中保持 HRM 和 LRM 图像之间的光谱一致性。为了减少由于 HRP 和 LRM 图像强度值之间的差异而发生的光谱失真，设计了一个新的空间光谱保真度项，以保持高分辨率空间中多光谱和全色像素之间的强度比与低分辨率空间相同。此外，采用总变差 (TV) 正则化项作为先验，以促进 HRM 频段中梯度的稀疏性。这些保真度项是在凸优化问题中制定的。然而，结构和 TV 项使这个优化问题不可微。因此，我们开发了一种有效的优化-最小化算法来解决优化问题。所提出的方法适用于 WorldView-3、Deimos-2 和 QuickBird 卫星获取的三个数据集。为了评估所提出方法的有效性，进行了视觉分析以及与各种全色锐化方法的定量比较。