The quadratic Wasserstein metric for inverse data matching
The quadratic Wasserstein metric for inverse data matching
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DOI：
10.1088/1361-6420/ab7e04
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发表时间：
2019-11
期刊：
影响因子：
2.1
通讯作者：
Bjorn Engquist;Kui Ren;Yunan Yang
中科院分区：
文献类型：
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作者：
Bjorn Engquist;Kui Ren;Yunan Yang
这项工作以分析和数值方式描述了二次 Wasserstein (W2) 距离作为逆问题计算解中数据差异度量的两个主要影响。首先，我们表明，在无限维设置中，W2 距离对反演过程具有平滑作用，使其对数据中的高频噪声具有鲁棒性，但会导致给定噪声水平下重建对象的分辨率降低。其次，我们证明，对于一些有限维问题，W2 距离导致的优化问题比经典的 L2 和 Ḣ−1 距离具有更好的凸性，使其成为解决此类逆匹配问题时更优选使用的距离。
This work characterizes, analytically and numerically, two major effects of the quadratic Wasserstein (W2) distance as the measure of data discrepancy in computational solutions of inverse problems. First, we show, in the infinite-dimensional setup, that the W2 distance has a smoothing effect on the inversion process, making it robust against high-frequency noise in the data but leading to a reduced resolution for the reconstructed objects at a given noise level. Second, we demonstrate that, for some finite-dimensional problems, the W2 distance leads to optimization problems that have better convexity than the classical L2 and Ḣ−1 distances, making it a more preferred distance to use when solving such inverse matching problems.