# Scattering Statistics of Generalized Spatial Poisson Point Processes

## TL;DR

This paper introduces a novel machine learning approach using Gabor-type measurements for analyzing inhomogeneous Poisson point processes, providing invariance to transformations and distinguishing them from other processes.

## Contribution

It proposes a new scattering transform based on Gabor measurements that decouples scale and frequency, enhancing analysis of Poisson point processes.

## Key findings

- Effectively distinguishes Poisson processes from self-similar processes
- Separates different types of Poisson point processes
- Provides invariance to translations and reflections

## Abstract

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.