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The Structure of Inverse Problems and Unnormalized Optimal Transport

  • Author(s): Puthawala, Michael Anthony
  • Advisor(s): Osher, Stanley J
  • et al.
Abstract

In this thesis we consider the solution of inverse problems, especially the components of a numerical inversion, and detection of forward operator error by the use of an extension optimal transport that accepts unnormalized arguments. We improve the inversion in wingen2015regularization in both speed and quality of reconstruction and motivated by the desire to improve reconstruction on experimental data we propose a method for fixing forward operator error. We introduce a new tool called the structure, based on the Wasserstein distance, and propose the use of this to diagnose and remedy forward operator error. Finally we extend the work of benamou2000computational and develop an Unnormalized Wasserstein distance measures the distance between two functions of possibly different integral.

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