On Stability of Linear Estimators in Poisson Noise

Alex Dytso; H. Vincent Poor

doi:10.1109/IEEECONF44664.2019.9048782

On Stability of Linear Estimators in Poisson Noise

Alex Dytso, H. Vincent Poor

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

1 Scopus citations

Abstract

This paper considers estimation of a random variable in Poisson noise. Specifically, the main focus is to assess optimality and near optimality conditions for linear estimators.In the first part of the paper, it is shown that linear estimators are optimal if and only if the underlying prior is a gamma distribution and the dark current parameter is zero.In the second part of the paper, a stability analysis of linear estimators is undertaken. Specifically, it is shown that if an optimal estimator is close to a linear estimator in an L_p,p ≥1 distance, then the underlying prior distribution is approximately gamma in the Lévy metric and the Kolmogorov metric.

Original language	English (US)
Title of host publication	Conference Record - 53rd Asilomar Conference on Circuits, Systems and Computers, ACSSC 2019
Editors	Michael B. Matthews
Publisher	IEEE Computer Society
Pages	670-674
Number of pages	5
ISBN (Electronic)	9781728143002
DOIs	https://doi.org/10.1109/IEEECONF44664.2019.9048782
State	Published - Nov 2019
Externally published	Yes
Event	53rd Asilomar Conference on Circuits, Systems and Computers, ACSSC 2019 - Pacific Grove, United States Duration: Nov 3 2019 → Nov 6 2019

Publication series

Name	Conference Record - Asilomar Conference on Signals, Systems and Computers
Volume	2019-November
ISSN (Print)	1058-6393

Conference

Conference	53rd Asilomar Conference on Circuits, Systems and Computers, ACSSC 2019
Country/Territory	United States
City	Pacific Grove
Period	11/3/19 → 11/6/19

All Science Journal Classification (ASJC) codes

Signal Processing
Computer Networks and Communications

Access to Document

10.1109/IEEECONF44664.2019.9048782

Cite this

Dytso, A., & Poor, H. V. (2019). On Stability of Linear Estimators in Poisson Noise. In M. B. Matthews (Ed.), Conference Record - 53rd Asilomar Conference on Circuits, Systems and Computers, ACSSC 2019 (pp. 670-674). Article 9048782 (Conference Record - Asilomar Conference on Signals, Systems and Computers; Vol. 2019-November). IEEE Computer Society. https://doi.org/10.1109/IEEECONF44664.2019.9048782

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title = "On Stability of Linear Estimators in Poisson Noise",

abstract = "This paper considers estimation of a random variable in Poisson noise. Specifically, the main focus is to assess optimality and near optimality conditions for linear estimators.In the first part of the paper, it is shown that linear estimators are optimal if and only if the underlying prior is a gamma distribution and the dark current parameter is zero.In the second part of the paper, a stability analysis of linear estimators is undertaken. Specifically, it is shown that if an optimal estimator is close to a linear estimator in an Lp,p ≥1 distance, then the underlying prior distribution is approximately gamma in the L{\'e}vy metric and the Kolmogorov metric.",

author = "Alex Dytso and Poor, {H. Vincent}",

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year = "2019",

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doi = "10.1109/IEEECONF44664.2019.9048782",

language = "English (US)",

series = "Conference Record - Asilomar Conference on Signals, Systems and Computers",

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Dytso, A & Poor, HV 2019, On Stability of Linear Estimators in Poisson Noise. in MB Matthews (ed.), Conference Record - 53rd Asilomar Conference on Circuits, Systems and Computers, ACSSC 2019., 9048782, Conference Record - Asilomar Conference on Signals, Systems and Computers, vol. 2019-November, IEEE Computer Society, pp. 670-674, 53rd Asilomar Conference on Circuits, Systems and Computers, ACSSC 2019, Pacific Grove, United States, 11/3/19. https://doi.org/10.1109/IEEECONF44664.2019.9048782

On Stability of Linear Estimators in Poisson Noise. / Dytso, Alex; Poor, H. Vincent.
Conference Record - 53rd Asilomar Conference on Circuits, Systems and Computers, ACSSC 2019. ed. / Michael B. Matthews. IEEE Computer Society, 2019. p. 670-674 9048782 (Conference Record - Asilomar Conference on Signals, Systems and Computers; Vol. 2019-November).

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

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AB - This paper considers estimation of a random variable in Poisson noise. Specifically, the main focus is to assess optimality and near optimality conditions for linear estimators.In the first part of the paper, it is shown that linear estimators are optimal if and only if the underlying prior is a gamma distribution and the dark current parameter is zero.In the second part of the paper, a stability analysis of linear estimators is undertaken. Specifically, it is shown that if an optimal estimator is close to a linear estimator in an Lp,p ≥1 distance, then the underlying prior distribution is approximately gamma in the Lévy metric and the Kolmogorov metric.

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On Stability of Linear Estimators in Poisson Noise

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