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

Alex Dytso, Michael Faus, H. Vincent Poor

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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.

Original languageEnglish (US)
Article number9201075
Pages (from-to)5894-5903
Number of pages10
JournalIEEE Transactions on Signal Processing
Volume68
DOIs
StatePublished - 2020

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Electrical and Electronic Engineering

Keywords

  • Conditional mean estimator
  • conjugate priors
  • estimation theory
  • gamma distribution
  • gaussian noise
  • vector poisson noise

Fingerprint Dive into the research topics of 'The Vector Poisson Channel: On the Linearity of the Conditional Mean Estimator'. Together they form a unique fingerprint.

Cite this