矩阵完备的松弛算法及其在地震走时数据插值中的应用
Relaxation algorithms for matrix completion, with applications to seismic travel-time data interpolation
摘要：
旅行时间层析成像用于通过拟合地面站收集的地震旅行时间数据来推断地球的基本三维波速结构。数据插值和去噪技术是重要的预处理步骤，其使用关于数据的先验知识，包括频域和小波域中的简约性、矩阵化的低秩结构和局部平滑性。我们展示了如何使用水平集优化公式将局部光滑结构与低秩约束相结合，并开发了一种新的松弛算法，可以有效地解决这些联合问题。在地震学环境中，我们使用该方法来插值缺失台站和去噪观测台站。新方法与其他算法相比具有竞争力，并提供了新的功能，在数据拟合约束的存在下，使用平滑度和低秩结构对观测数据进行插值。
英文摘要：
Travel time tomography is used to infer the underlying three-dimensional wavespeed structure of the Earth by fitting seismic travel time data collected at surface stations. Data interpolation and denoising techniques are important pre-processing steps that use prior knowledge about the data, including parsimony in the frequency and wavelet domains, low-rank structure of matricizations, and local smoothness. We show how local smoothness structure can be combined with low rank constraints using level-set optimization formulations, and develop a new relaxation algorithm that can efficiently solve these joint problems. In the seismology setting, we use the approach to interpolate missing stations and de-noise observed stations. The new approach is competitive with alternative algorithms, and offers new functionality to interpolate observed data using both smoothness and low rank structure in the presence of data fitting constraints.
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