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arXiv · 2106.02146

The Signed Cumulative Distribution Transform for 1-D Signal Analysis and Classification

Akram Aldroubi·Rocio Diaz Martin·Ivan Medri·Gustavo K. Rohde·Sumati Thareja
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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 $\overline{\mathbb{R}}$. 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.

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Akram Aldroubi, Rocio Diaz Martin, Ivan Medri, Gustavo K. Rohde, Sumati Thareja. 2021-06-03. The Signed Cumulative Distribution Transform for 1-D Signal Analysis and Classification. https://doi.org/10.3934/fods.2022001

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