The Vector Poisson Channel: On the Linearity of the Conditional Mean Estimator

Document Type

Article

Publication Date

1-1-2020

Abstract

This work studies properties of the conditional mean estimator in vector Poisson noise. The main emphasis is to study conditions on prior distributions that induce linearity of the conditional mean estimator. The paper consists of two main results. The first result shows that the only distribution that induces the linearity of the conditional mean estimator is a product gamma distribution. Moreover, it is shown that the conditional mean estimator cannot be linear when the dark current parameter of the Poisson noise is non-zero. The second result produces a quantitative refinement of the first result. Specifically, it is shown that if the conditional mean estimator is close to linear in a mean squared error sense, then the prior distribution must be close to a product gamma distribution in terms of their Laplace transforms. Finally, the results are compared to their Gaussian counterparts.

Identifier

85087496816 (Scopus)

Publication Title

IEEE Transactions on Signal Processing

External Full Text Location

https://doi.org/10.1109/TSP.2020.3025525

e-ISSN

19410476

ISSN

1053587X

First Page

5894

Last Page

5903

Volume

68

Grant

CCF-1908308

Fund Ref

National Science Foundation

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