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arXiv 2506.04869cs.CV

通过图像修复视角进行地质场恢复

Geological Field Restoration through the Lens of Image Inpainting

AIRI;Skoltech(斯科尔科沃科学技术学院);Sberbank of Russia(俄罗斯联邦储蓄银行)

Vladislav Trifonov, Ivan Oseledets, Ekaterina Muravleva

AI总结:

研究在有限观测下地质场重建问题,借鉴图像修复方法,将部分观测空间场建模为多维张量,通过全局低秩结构与空间平滑性恢复缺失值,实验表明在SPE10模型上优于普通克里金法。

摘要:

我们研究了一个在有限观测下进行地质场重建的不正问题。工程师常需从稀疏测量如勘探井数据中重建地下地质场。受图像修复启发,我们将部分观测的空间场建模为多维张量,并通过强制全局低秩结构和空间平滑性来恢复缺失值。我们通过交替方向乘子法求解所得到的优化问题。在SPE10模型2基准上,这种确定性方法在各种采样密度下均产生比普通克里金法更低的相对平方误差,并产生视觉上一致的重建结果。

英文摘要:

We study an ill-posed problem of geological field reconstruction under limited observations. Engineers often have to deal with the problem of reconstructing the subsurface geological field from sparse measurements such as exploration well data. Inspired by image inpainting, we model this partially observed spatial field as a multidimensional tensor and recover missing values by enforcing a global low rank structure together with spatial smoothness. We solve the resulting optimization via the Alternating Direction Method of Multipliers. On the SPE10 model 2 benchmark, this deterministic approach yields consistently lower relative squared error than ordinary kriging across various sampling densities and produces visually coherent reconstructions.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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