The quadratic Wasserstein metric for inverse data matching

Abstract

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 distances, making it a more preferred distance to use when solving such inverse matching problems.