The Quadratic Wasserstein Metric for Inverse Data Matching Problems

Monday, November 9, 2020 - 9:30am - 10:15am
Yunan Yang (New York University)
This talk focus on 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 metric 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 metric leads to better convexity for optimization problems than the classical Sobolev norms, making it a more preferred objective function when solving such inverse matching problems.