The Signed Cumulative Distribution Transform for 1-D signal analysis and classification
Akram Aldroubi, Rocío Díaz Martín, Iván Medri, Gustavo Kunde Rohde, Sumati Thareja · Foundations of Data Science · 2022
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 [ 29 ] to arbitrary (signed) signals on \begin{document}$ \overline {\mathbb{R}} $\end{document} . 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.