Cramér–Rao lower bounds on the performance of charge-coupled-device optical position estimators

Winick, Kim A.

doi:10.1364/josaa.3.001809

Cited by 88 publications

(70 citation statements)

References 9 publications

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“…This framework extends previous work applying Fisher information to individual imaging techniques (e.g., Helstrom, 1969;Winick, 1986;Ober et al, 2004;Aguet et al, 2005;Shahram, 2005;Shahram and Milanfar, 2006;Marengo et al, 2009;Sanches et al, 2010;Mukamel and Schnitzer, 2012;Quirin et al, 2012;Shechtman et al, 2014). For example, many studies have used Fisher information to examine the theoretical optimal resolution of specific optical imaging techniques (Helstrom, 1969;Winick, 1986;Ober et al, 2004;Aguet et al, 2005;Shahram, 2005;Shahram and Milanfar, 2006;Marengo et al, 2009;Mukamel and Schnitzer, 2012;Quirin et al, 2012;Shechtman et al, 2014). However, using Fisher information to optimize other neural recording technologies, while occasionally done (e.g., MRI in Sanches et al, 2010), is not as common.…”

Section: Framework Discussionsupporting

confidence: 63%

Spatial Information in Large-Scale Neural Recordings

Cybulski¹,

Glaser²,

Marblestone

et al. 2014

Preprint

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To record from a given neuron, a recording technology must be able to separate the activity of that neuron from the activity of its neighbors. Here, we develop a Fisher information based framework to determine the conditions under which this is feasible for a given technology. This framework combines measurable point spread functions with measurable noise distributions to produce theoretical bounds on the precision with which a recording technology can localize neural activities. If there is sufficient information to uniquely localize neural activities, then a technology will, from an information theoretic perspective, be able to record from these neurons. We (1) describe this framework, and (2) demonstrate its application in model experiments. This method generalizes to many recording devices that resolve objects in space and should be useful in the design of next-generation scalable neural recording systems.

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Section: Framework Discussionsupporting

confidence: 63%

Spatial Information in Large-Scale Neural Recordings

Cybulski¹,

Glaser²,

Marblestone

et al. 2014

Preprint

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“…Note that in the above expressions no assumptions are made about the size or shape of the pixels. In Winick (1986) an expression was derived that is essentially a special case of Eq. 37, i.e.…”

Section: Effects Of Pixelationmentioning

confidence: 99%

“…In Winick (1986) the Cramer Rao lower bound was calculated for a position estimation problem in the special case where the image of the object is given by a Gaussian function and the detector is pixelated.…”

Section: Introductionmentioning

confidence: 99%

A Stochastic Analysis of Performance Limits for Optical Microscopes

Ram

Ward

Ober

2006

Multidim Syst Sign Process

219

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The optical microscope is a powerful instrument for observing cellular events. Recently, the increased use of microscopy in quantitative biological research, including single molecule microscopy, has generated significant interest in determining the performance limits of an optical microscope. Here, we formulate this problem in the context of a parameter estimation approach in which the acquired imaging data is modeled as a spatio-temporal stochastic process. We derive formulations of the Fisher information matrix for models that allow both stationary and moving objects. The effects of background signal, detector size, pixelation and noise sources are also considered. Further, formulations are given that allow the study of defocused objects. Applications are discussed for the special case of the estimation of the location of objects, especially single molecules. Specific emphasis is placed on the derivation of conditions that guarantee block diagonal or diagonal Fisher information matrices.

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“…Poisson process 3 with the average number of electrons given by Aas,,m(1, 2) + AN where A, is the average number of photoelectrons produced by a target of unit intensity, and AN is the average number of photoelectrons produced by the sum of the two noise processes. The noise is assumed to be spatially and temporally independent and stationary.…”

Section: The Cramtr-rao Boundsmentioning

confidence: 99%

Cramer-Rao Bounds on the Accuracy of Location and Velocity Estimations Using CCD Optical Sensors

Chen¹

1987

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Cramér–Rao lower bounds on the performance of charge-coupled-device optical position estimators

Cited by 88 publications

References 9 publications

Spatial Information in Large-Scale Neural Recordings

Spatial Information in Large-Scale Neural Recordings

A Stochastic Analysis of Performance Limits for Optical Microscopes

Cramer-Rao Bounds on the Accuracy of Location and Velocity Estimations Using CCD Optical Sensors

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