A state space based approach to localizing single molecules from multi-emitter images

Milad R. Vahid; Jerry Chao; E. Sally Ward; Raimund J. Ober

doi:10.1117/12.2253175

17 February 2017 A state space based approach to localizing single molecules from multi-emitter images

Milad R. Vahid, Jerry Chao, E. Sally Ward, Raimund J. Ober

Proceedings Volume 10070, Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing XXIV; 100700J (2017) https://doi.org/10.1117/12.2253175
Event: SPIE BiOS, 2017, San Francisco, California, United States

Abstract

Single molecule super-resolution microscopy is a powerful tool that enables imaging at sub-diffraction-limit resolution. In this technique, subsets of stochastically photoactivated fluorophores are imaged over a sequence of frames and accurately localized, and the estimated locations are used to construct a high-resolution image of the cellular structures labeled by the fluorophores. Available localization methods typically first determine the regions of the image that contain emitting fluorophores through a process referred to as detection. Then, the locations of the fluorophores are estimated accurately in an estimation step. We propose a novel localization method which combines the detection and estimation steps. The method models the given image as the frequency response of a multi-order system obtained with a balanced state space realization algorithm based on the singular value decomposition of a Hankel matrix, and determines the locations of intensity peaks in the image as the pole locations of the resulting system. The locations of the most significant peaks correspond to the locations of single molecules in the original image. Although the accuracy of the location estimates is reasonably good, we demonstrate that, by using the estimates as the initial conditions for a maximum likelihood estimator, refined estimates can be obtained that have a standard deviation close to the Cramér-Rao lower bound-based limit of accuracy. We validate our method using both simulated and experimental multi-emitter images.

Citation Download Citation

Milad R. Vahid, Jerry Chao, E. Sally Ward, and Raimund J. Ober "A state space based approach to localizing single molecules from multi-emitter images", Proc. SPIE 10070, Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing XXIV, 100700J (17 February 2017); https://doi.org/10.1117/12.2253175

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