基于稀疏部分数据的运动源确定性统计重建方法
A deterministic-statistical approach to reconstruct moving sources using sparse partial data
摘要：
我们考虑使用部分测量数据的运动源的重建。提出了一种两步确定性统计方法。在第一步中，一个近似的直接采样方法，以获得在不同的时间的源的位置。这些信息被编码在先验中，这对于贝叶斯方法在第二步中的成功至关重要。在Hellinger距离的意义下分析了后验测度的适定性。这两个步骤都基于相同的物理模型，并使用相同的测量数据集。数值算例表明，该方法继承了确定性方法和贝叶斯反演方法的优点。
英文摘要：
We consider the reconstruction of moving sources using partial measured data. A two-step deterministic-statistical approach is proposed. In the first step, an approximate direct sampling method is developed to obtain the locations of the sources at different times. Such information is coded in the priors, which is critical for the success of the Bayesian method in the second step. The well-posedness of the posterior measure is analyzed in the sense of the Hellinger distance. Both steps are based on the same physical model and use the same set of measured data. The combined approach inherits the merits of the deterministic method and Bayesian inversion as demonstrated by the numerical examples.
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