Pansharpening aims to fuse low-resolution multi-spectral image and high-resolution panchromatic (PAN) image to produce a high-resolution multi-spectral (HRMS) image. In this paper, a new residual learning network based on gradient transformation prior, termed as GTP-PNet, is proposed to generate the high-quality HRMS image with accurate spectral distribution as well as reasonable spatial structure. Different from previous deep models that only rely on supervision of the HRMS reference image, we introduce the gradient transformation prior to the deep model, so as to improve the solution accuracy. Our model consists of two networks, namely gradient transformation network (TNet) and pansharpening network (PNet). TNet is committed to seeking the nonlinear mapping between gradients of PAN and HRMS images, which is essentially a spatial relationship regression of imaging bands in different ranges. PNet is the residual learning network used to generate the HRMS image, which is not only supervised by the HRMS reference image, but also constrained by the trained TNet. As a result, the HRMS image generated by PNet not only approximates the HRMS reference image in the spectral distribution, but also conforms to the gradient transformation prior in the spatial structure. Experimental results demonstrate the significant superiority of our method over the current state-of-the-arts in terms of both subjective visual effect and quantitative metrics. We also apply our method to produce the HR normalized difference vegetation index in remote sensing, which can achieve the best performance. Moreover, our method is much competitive compared with the state-of-the-art alternatives in running efficiency.

Pansharpening的目的是融合低分辨率多光谱图像和高分辨率全色（PAN）图像，以生成高分辨率多光谱（HRMS）图像。本文提出了一种基于梯度变换先验的残差学习网络，称为GTP-PNet。提出了一种生成具有准确光谱分布和合理空间结构的高质量HRMS图像的方法。与以前仅依靠HRMS参考图像的监督的深层模型不同，我们在深层模型之前引入了梯度变换，以提高求解精度。我们的模型由两个网络组成，即梯度转换网络（TNet）和泛锐化网络（PNet）。TNet致力于寻求PAN和HRMS图像的梯度之间的非线性映射，这本质上是不同范围成像带的空间关系回归。PNet是用于生成HRMS图像的残余学习网络，不仅受HRMS参考图像监督，而且受训练的TNet约束。结果是，PNet生成的HRMS图像不仅在光谱分布中近似HRMS参考图像，而且在空间结构上符合先验的梯度变换。实验结果表明，就主观视觉效果和定量指标而言，我们的方法相对于当前的最新技术具有明显的优势。我们还应用我们的方法在遥感中产生了HR归一化差异植被指数，可以达到最佳性能。此外，在运行效率方面，我们的方法与最先进的替代方法相比更具竞争力。实验结果表明，就主观视觉效果和定量指标而言，我们的方法相对于当前的最新技术具有明显的优势。我们还应用我们的方法在遥感中产生了HR归一化差异植被指数，可以达到最佳性能。此外，在运行效率方面，我们的方法与最先进的替代方法相比更具竞争力。实验结果表明，就主观视觉效果和定量指标而言，我们的方法相对于当前的最新技术具有明显的优势。我们还应用我们的方法在遥感中产生了HR归一化差异植被指数，可以达到最佳性能。此外，在运行效率方面，我们的方法与最先进的替代方法相比更具竞争力。