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A stochastic analysis of distance estimation approaches in single molecule microscopy: Quantifying the resolution limits of photon-limited imaging systems

A stochastic analysis of distance estimation approaches in single molecule microscopy: Quantifying the resolution limits of photon-limited imaging systems
A stochastic analysis of distance estimation approaches in single molecule microscopy: Quantifying the resolution limits of photon-limited imaging systems

Optical microscopy is an invaluable tool to visualize biological processes at the cellular scale. In the recent past, there has been significant interest in studying these processes at the single molecule level. An important question that arises in single molecule experiments concerns the estimation of the distance of separation between two closely spaced molecules. Presently, there exists different experimental approaches to estimate the distance between two single molecules. However, it is not clear as to which of these approaches provides the best accuracy for estimating the distance. Here, we address this problem rigorously by using tools of statistical estimation theory. We derive formulations of the Fisher information matrix for the underlying estimation problem of determining the distance of separation from the acquired data for the different approaches. Through the Cramer-Rao inequality, we derive a lower bound to the accuracy with which the distance of separation can be estimated. We show through Monte-Carlo simulations that the bound can be attained by the maximum likelihood estimator. Our analysis shows that the distance estimation problem is in fact related to the localization accuracy problem, the latter being a distinct problem that deals with how accurately the location of an object can be determined. We have carried out a detailed investigation of the relationship between the Fisher information matrices of the two problems for the different experimental approaches considered here. The paper also addresses the issue of a singular Fisher information matrix, which presents a significant complication when calculating the Cramer-Rao lower bound. Here, we show how experimental design can overcome the singularity. Throughout the paper, we illustrate our results by considering a specific image profile that describe the image of a single molecule.

Fluorescence microscopy, Marked point process, Performance bounds, Photon statistics, Rayleigh's criterion, Resolution limits
0923-6082
503-542
Ram, Sripad
559bd560-3817-4e53-8c7a-2f08e4518412
Ward, E. Sally
b31c0877-8abe-485f-b800-244a9d3cd6cc
Ober, Raimund J.
31f4d47f-fb49-44f5-8ff6-87fc4aff3d36
Ram, Sripad
559bd560-3817-4e53-8c7a-2f08e4518412
Ward, E. Sally
b31c0877-8abe-485f-b800-244a9d3cd6cc
Ober, Raimund J.
31f4d47f-fb49-44f5-8ff6-87fc4aff3d36

Ram, Sripad, Ward, E. Sally and Ober, Raimund J. (2013) A stochastic analysis of distance estimation approaches in single molecule microscopy: Quantifying the resolution limits of photon-limited imaging systems. Multidimensional Systems and Signal Processing, 24 (3), 503-542. (doi:10.1007/s11045-012-0175-6).

Record type: Article

Abstract

Optical microscopy is an invaluable tool to visualize biological processes at the cellular scale. In the recent past, there has been significant interest in studying these processes at the single molecule level. An important question that arises in single molecule experiments concerns the estimation of the distance of separation between two closely spaced molecules. Presently, there exists different experimental approaches to estimate the distance between two single molecules. However, it is not clear as to which of these approaches provides the best accuracy for estimating the distance. Here, we address this problem rigorously by using tools of statistical estimation theory. We derive formulations of the Fisher information matrix for the underlying estimation problem of determining the distance of separation from the acquired data for the different approaches. Through the Cramer-Rao inequality, we derive a lower bound to the accuracy with which the distance of separation can be estimated. We show through Monte-Carlo simulations that the bound can be attained by the maximum likelihood estimator. Our analysis shows that the distance estimation problem is in fact related to the localization accuracy problem, the latter being a distinct problem that deals with how accurately the location of an object can be determined. We have carried out a detailed investigation of the relationship between the Fisher information matrices of the two problems for the different experimental approaches considered here. The paper also addresses the issue of a singular Fisher information matrix, which presents a significant complication when calculating the Cramer-Rao lower bound. Here, we show how experimental design can overcome the singularity. Throughout the paper, we illustrate our results by considering a specific image profile that describe the image of a single molecule.

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More information

Accepted/In Press date: 8 January 2012
e-pub ahead of print date: 26 January 2012
Published date: September 2013
Keywords: Fluorescence microscopy, Marked point process, Performance bounds, Photon statistics, Rayleigh's criterion, Resolution limits

Identifiers

Local EPrints ID: 423641
URI: http://eprints.soton.ac.uk/id/eprint/423641
ISSN: 0923-6082
PURE UUID: c6e1ccc9-3579-4a76-9959-21840d06f8a5
ORCID for E. Sally Ward: ORCID iD orcid.org/0000-0003-3232-7238
ORCID for Raimund J. Ober: ORCID iD orcid.org/0000-0002-1290-7430

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Date deposited: 27 Sep 2018 16:30
Last modified: 18 Mar 2024 03:48

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Contributors

Author: Sripad Ram
Author: E. Sally Ward ORCID iD
Author: Raimund J. Ober ORCID iD

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