Abstract: In the field of indefinite spatial data reconstruction, Multiple-Point Statistics (MPS) has been widely used, but its applicability is affected due to the high computational cost. A spatial data reconstruction method based on a multi-resolution Generative Adversarial Network (GAN) model was proposed by using a pyramid structured fully convolutional GAN model to learn the data training images with different resolutions. In the method, the detailed features were captured from high-resolution training images and large-scale features were captured from low-resolution training images. Therefore, the image reconstructed by this method contained the global and local structural information of the training image while maintaining a certain degree of randomness. By comparing the proposed algorithm with the representative algorithms in MPS and the GAN method applied in spatial data reconstruction, it can be seen that the total time of 10 reconstructions of the proposed algorithm is reduced by about 1 h, the difference between the average porosity of the algorithm and the training image porosity is reduced to 0.000 2, and the variogram curve and the Multi-Point Connectivity (MPC) curve of the algorithm are closer to those of the training image, showing that the proposed algorithm has better reconstruction quality.

Key words: spatial data, multi-resolution, Generative Adversarial Network (GAN), training image, reconstruction

摘要： 在空间数据不确定性重建领域，多点统计法（MPS）得到了广泛的应用，但由于计算成本较高，其适用性受到了影响。通过使用金字塔结构的全卷积生成对抗网络（GAN）模型学习不同分辨率的训练图像，提出了一种基于多分辨率GAN模型的空间数据重建方法。该方法从高分辨率训练图像中捕获细节特征，从低分辨率训练图像中捕获大范围特征，因此该方法重建的图像包含训练图像的全局和局部结构信息，同时保持一定的随机性。把所提算法与MPS中的代表性算法以及应用于空间数据重建的GAN方法进行对比的结果表明，所提方法10次重建的总时间降低了约1 h，其平均孔隙度与训练图像孔隙度的差值降低至0.000 2，并且其变差函数曲线和多点连接性函数（MPC）曲线更接近于训练图像，可见所提算法重建质量更好。

关键词: 空间数据, 多分辨率, 生成对抗网络, 训练图像, 重建