Abstract
We present a new viewpoint on a reconstructing multidimensional geological fields from sparse observations. Drawing inspiration from deterministic image inpainting techniques, we model a partially observed spatial field as a multidimensional tensor and recover missing values by enforcing a global low-rank structure. Our approach combines ideas from tensor completion and geostatistics, providing a robust optimization framework. Experiments on synthetic geological fields demonstrate that used tensor completion method significant improvements in reconstruction accuracy over ordinary kriging for various percent of observed data.
Abstract (translated)
我们提出了一种从稀疏观测数据重建多维地质场的新视角。借鉴确定性图像插值技术的灵感，我们将部分观察到的空间场建模为一个多维张量，并通过强制执行全局低秩结构来恢复缺失值。我们的方法结合了张量补全和地质统计学的思想，提供了一个稳健的优化框架。在合成地质领域的实验表明，所使用的张量补全方法相比于普通克里金插值法，在各种观测数据百分比下显著提高了重建准确性。
URL
https://arxiv.org/abs/2506.04869
