The quadratic Wasserstein metric for inverse data matching
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This work characterizes, analytically and numerically, two major effects of the quadratic Wasserstein (W_2) distance as the measure of data discrepancy in computational solutions of inverse problems. First, we show, in the infinite-dimensional setup, that the W_2 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 W_2 distance leads to optimization problems that have better convexity than the classical L^2 and Ḣ^-1 distances, making it a more preferred distance to use when solving such inverse matching problems.
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