Publication 16-CNA-023

A Transportation $L^p$ Distance for Signal Analysis

Matthew Thorpe
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
mthorpe@andrew.cmu.edu

Serim Park
Carnegie Mellon University
Pittsburgh, PA 15213

Soheil Kolouri
HRL Laboratories
Malibu, CA 90265, USA

Gustavo K. Rohde
University of Virginia
Charlottesville, VA 22908, USA

Dejan Slepčev
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
slepcev@andrew.cmu.edu

Abstract: Transport based distances, such as the Wasserstein distance and earth mover's distance, have been shown to be an effective tool in signal and image analysis. The success of transport based distances is in part due to their Lagrangian nature which allows it to capture the important variations in many signal classes. However these distances require the signal to be nonnegative and normalized. Furthermore, the signals are considered as measures and compared by redistributing (transporting) them, which does not directly take into account the signal intensity. Here we study a transport-based distance, called the $TL^p$ distance, that combines Lagrangian and intensity modelling and is directly applicable to general,non-positive and multi-channelled signals. The framework allows the application of existing numerical methods. We give an overview of the basic properties of this distance and applications to classification, with multi-channelled, non-positive one and two-dimensional signals, and color transfer.

Get the paper in its entirety as  16-CNA-023.pdf

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