Scattering Statistics of Generalized Spatial Poisson Point Processes
This work addresses the analysis of random signals for applications in fields like signal processing or statistics, but it appears incremental as it builds upon the wavelet scattering transform with modifications.
The paper tackles the problem of analyzing randomly generated discrete signals modeled as inhomogeneous, compound Poisson point processes by introducing a machine learning model that is invariant to translations and reflections, decouples scale and frequency using Gabor-type measurements, and distinguishes Poisson point processes from self-similar processes and different types of Poisson processes.
We present a machine learning model for the analysis of randomly generated discrete signals, modeled as the points of an inhomogeneous, compound Poisson point process. Like the wavelet scattering transform introduced by Mallat, our construction is naturally invariant to translations and reflections, but it decouples the roles of scale and frequency, replacing wavelets with Gabor-type measurements. We show that, with suitable nonlinearities, our measurements distinguish Poisson point processes from common self-similar processes, and separate different types of Poisson point processes.