NDLI: An EM Approach for Time-Variant Poisson-Gaussian Model Parameter Estimation

Content Provider	IEEE Xplore Digital Library
Author	Jezierska, A. Chaux, C. Pesquet, J.-C. Talbot, H. Engler, G.
Copyright Year	1991
Abstract	The problem of estimating the parameters of a Poisson-Gaussian model from experimental data has recently raised much interest in various applications, for instance in confocal fluorescence microscopy. In this context, a field of independent random variables is observed, which is varying both in time and space. Each variable is a sum of two components, one following a Poisson and the other a Gaussian distribution. In this paper, a general formulation is considered where the associated Poisson process is nonstationary in space and also exhibits an exponential decay in time, whereas the Gaussian component corresponds to a stationary white noise with arbitrary mean. To solve the considered parametric estimation problem, we follow an iterative Expectation-Maximization (EM) approach. The parameter update equations involve deriving finite approximation of infinite sums. Expressions for the maximum error incurred in the process are also given. Since the problem is non-convex, we pay attention to the EM initialization, using a moment-based method where recent optimization tools come into play. We carry out a performance analysis by computing the Cramer-Rao bounds on the estimated variables. The practical performance of the proposed estimation procedure is illustrated on both synthetic data and real fluorescence macroscopy image sequences. The algorithm is shown to provide reliable estimates of the mean/variance of the Gaussian noise and of the scale parameter of the Poisson component, as well as of its exponential decay rate. In particular, the mean estimate of the Poisson component can be interpreted as a good-quality denoised version of the data.
Sponsorship	IEEE Signal Processing Society
Starting Page	17
Ending Page	30
Page Count	14
File Size	4872115
File Format	PDF
ISSN	1053587X
Volume Number	62
Issue Number	1
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2014-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Noise Estimation Random variables Indexes Vectors Data models Parameter estimation Poisson-Gaussian noise Cramer-Rao bounds expectation-maximization microscopy optimization parametric estimation
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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