The quadratic Wasserstein metric for earthquake location

TL;DR: It is demonstrated that for some finite-dimensional problems, the quadratic Wasserstein distance leads to optimization problems that have better convexity than the classical $L^2$ and $H^{-1}$ distances, making it a more preferred distance to use when solving such inverse matching problems.

TL;DR: In this paper, the convexity of the Wasserstein metric as the objective function was shown to be an important property for full waveform inversion (FWI) using optimal transport.

TL;DR: This work pulls back the $L^2$-Wasserstein metric tensor in probability density space to parameter space, under which the parameter space become a Riemannian manifold, named the Wasserstein statistical manifold, and derives the gradient flow and natural gradient descent method in parameter space.

TL;DR: This work proposes using the quadratic Wasserstein metric as a new misfit function in FWI, and points to the advantages of using optimal transport over the least-squares norm will be discussed.

TL;DR: In this article, the problem of least square problems with non-linear normal equations is solved by an extension of the standard method which insures improvement of the initial solution, which can also be considered an extension to Newton's method.

TL;DR: The aim of this book is to provide a Discussion of Constrained Optimization and its Applications to Linear Programming and Other Optimization Problems.

TL;DR: Independent component analysis as mentioned in this paper is a statistical generative model based on sparse coding, which is basically a proper probabilistic formulation of the ideas underpinning sparse coding and can be interpreted as providing a Bayesian prior.