SCATTERING STATISTICS OF GENERALIZED SPATIAL POISSON POINT PROCESSES

Michael Perlmutter; Jieqian He; Matthew Hirn

doi:10.1109/ICASSP43922.2022.9746382

SCATTERING STATISTICS OF GENERALIZED SPATIAL POISSON POINT PROCESSES

Michael Perlmutter, Jieqian He, Matthew Hirn

Mathematics Department

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

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.

Original language	English
Title of host publication	2022 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2022 - Proceedings
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	5528-5532
Number of pages	5
ISBN (Electronic)	9781665405409
DOIs	https://doi.org/10.1109/ICASSP43922.2022.9746382
State	Published - 2022
Event	2022 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2022 - Hybrid, Singapore Duration: 22 May 2022 → 27 May 2022

Publication series

Name	ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume	2022-May
ISSN (Print)	1520-6149

Conference

Conference	2022 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2022
Country/Territory	Singapore
City	Hybrid
Period	22/05/22 → 27/05/22

Keywords

Poisson point process
Scattering transform
convolutional neural network

Access to Document

10.1109/ICASSP43922.2022.9746382

Cite this

Perlmutter, M., He, J., & Hirn, M. (2022). SCATTERING STATISTICS OF GENERALIZED SPATIAL POISSON POINT PROCESSES. In 2022 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2022 - Proceedings (pp. 5528-5532). (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings; Vol. 2022-May). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICASSP43922.2022.9746382

Perlmutter, Michael ; He, Jieqian ; Hirn, Matthew. / SCATTERING STATISTICS OF GENERALIZED SPATIAL POISSON POINT PROCESSES. 2022 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2022 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2022. pp. 5528-5532 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings).

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title = "SCATTERING STATISTICS OF GENERALIZED SPATIAL POISSON POINT PROCESSES",

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.",

keywords = "Poisson point process, Scattering transform, convolutional neural network",

author = "Michael Perlmutter and Jieqian He and Matthew Hirn",

note = "Publisher Copyright: {\textcopyright} 2022 IEEE; 2022 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2022 ; Conference date: 22-05-2022 Through 27-05-2022",

year = "2022",

doi = "10.1109/ICASSP43922.2022.9746382",

language = "English",

series = "ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "5528--5532",

booktitle = "2022 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2022 - Proceedings",

}

Perlmutter, M, He, J & Hirn, M 2022, SCATTERING STATISTICS OF GENERALIZED SPATIAL POISSON POINT PROCESSES. in 2022 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2022 - Proceedings. ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, vol. 2022-May, Institute of Electrical and Electronics Engineers Inc., pp. 5528-5532, 2022 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2022, Hybrid, Singapore, 22/05/22. https://doi.org/10.1109/ICASSP43922.2022.9746382

SCATTERING STATISTICS OF GENERALIZED SPATIAL POISSON POINT PROCESSES. / Perlmutter, Michael; He, Jieqian; Hirn, Matthew.
2022 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2022 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2022. p. 5528-5532 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings; Vol. 2022-May).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - SCATTERING STATISTICS OF GENERALIZED SPATIAL POISSON POINT PROCESSES

AU - Perlmutter, Michael

AU - He, Jieqian

AU - Hirn, Matthew

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

KW - Poisson point process

KW - Scattering transform

KW - convolutional neural network

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U2 - 10.1109/ICASSP43922.2022.9746382

DO - 10.1109/ICASSP43922.2022.9746382

M3 - Conference contribution

AN - SCOPUS:85131236854

T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings

SP - 5528

EP - 5532

BT - 2022 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2022 - Proceedings

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2022

Y2 - 22 May 2022 through 27 May 2022

ER -

Perlmutter M, He J, Hirn M. SCATTERING STATISTICS OF GENERALIZED SPATIAL POISSON POINT PROCESSES. In 2022 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2022 - Proceedings. Institute of Electrical and Electronics Engineers Inc. 2022. p. 5528-5532. (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). doi: 10.1109/ICASSP43922.2022.9746382

SCATTERING STATISTICS OF GENERALIZED SPATIAL POISSON POINT PROCESSES

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Keywords

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