Transport-based analysis, modeling, and learning from signal and data distributions

Abstract

Transport-based techniques for signal and data analysis have received increased attention recently. Given their abilities to provide accurate generative models for signal intensities and other data distributions, they have been used in a variety of applications including content-based retrieval, cancer detection, image super-resolution, and statistical machine learning, to name a few, and shown to produce state of the art in several applications. Moreover, the geometric characteristics of transport-related metrics have inspired new kinds of algorithms for interpreting the meaning of data distributions. Here we provide an overview of the mathematical underpinnings of mass transport-related methods, including numerical implementation, as well as a review, with demonstrations, of several applications.

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Cited by in corpus (7)

• Application of Optimal Transport and the Quadratic Wasserstein Metric to Full-Waveform Inversion
• An optimal transport model for imaging in atmospheric turbulence
• Optimal Transport Based Seismic Inversion: Beyond Cycle Skipping
• Analysis and Application of Optimal Transport For Challenging Seismic Inverse Problems
• A Transportation $L^p$ Distance for Signal Analysis
• Misfit function for full waveform inversion based on Earth Mover's Distance with dynamic formulation
• Transport-Based Pattern Theory: A Signal Transformation Approach