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Convexity Of Regularized Optimal Transport Dissimilarity Measures For Signed Signals, Christian P. Fowler

Mathematics & Statistics ETDs

Debiased Sinkhorn divergence (DS divergence) is a distance function of

regularized optimal transport that measures the dissimilarity between two

probability measures of optimal transport. This thesis analyzes the advantages of

using DS divergence when compared to the more computationally expensive

Wasserstein distance as well as the classical Euclidean norm. Specifically, theory

and numerical experiments are used to show that Debiased Sinkhorn divergence

has geometrically desirable properties such as maintained convexity after data

normalization. Data normalization is often needed to calculate Sinkhorn

divergence as well as Wasserstein distance, as these formulas only accept

probability distributions as inputs and do not directly …

Optimal Transport Driven Bayesian Inversion With Application To Signal Processing, Elijah F. Perez

Mathematics & Statistics ETDs

This paper will outline a Debiased Sinkhorn Divergence driven Bayesian inversion framework. Conventionally, a Gaussian Driven Bayesian framework is used when performing Bayesian inversion. A major issue with this Gaussian framework is that the Gaussian likelihood, driven by the L2 norm, is not affected by phase shift in a given signal. This issue has been addressed in [1] using a Wasserstein framework. However, the Wasserstein framework still has an issue because it assumes statistical independence when multidimensional signals are analyzed. This assumption of statistical independence cannot always be made when analyzing signals where multiple detectors are recording one event, say …