The Signed Cumulative Distribution Transform for 1-D Signal Analysis and Classification
Information Theory
2022-07-19 v1 Machine Learning
Functional Analysis
math.IT
Abstract
This paper presents a new mathematical signal transform that is especially suitable for decoding information related to non-rigid signal displacements. We provide a measure theoretic framework to extend the existing Cumulative Distribution Transform [ACHA 45 (2018), no. 3, 616-641] to arbitrary (signed) signals on . We present both forward (analysis) and inverse (synthesis) formulas for the transform, and describe several of its properties including translation, scaling, convexity, linear separability and others. Finally, we describe a metric in transform space, and demonstrate the application of the transform in classifying (detecting) signals under random displacements.
Cite
@article{arxiv.2106.02146,
title = {The Signed Cumulative Distribution Transform for 1-D Signal Analysis and Classification},
author = {Akram Aldroubi and Rocio Diaz Martin and Ivan Medri and Gustavo K. Rohde and Sumati Thareja},
journal= {arXiv preprint arXiv:2106.02146},
year = {2022}
}