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Biomed Opt Express. 2017 Feb 6;8(3):1332-1355. doi: 10.1364/BOE.8.001332. eCollection 2017 Mar 1.

State space approach to single molecule localization in fluorescence microscopy.

Vahid MR1,2, Chao J1,2, Kim D1,2, Ward ES2,3, Ober RJ1,2.

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Department of Biomedical Engineering, Texas A&M University, College Station, TX 77843, USA.
Department of Molecular and Cellular Medicine, Texas A&M Health Science Center, College Station, TX 77843, USA.
Department of Microbial Pathogenesis and Immunology, Texas A&M Health Science Center, College Station, TX 77843, USA.


Single molecule super-resolution microscopy enables imaging at sub-diffraction-limit resolution by producing images of subsets of stochastically photoactivated fluorophores over a sequence of frames. In each frame of the sequence, the fluorophores are accurately localized, and the estimated locations are used to construct a high-resolution image of the cellular structures labeled by the fluorophores. Many methods have been developed for localizing fluorophores from the images. The majority of these methods comprise two separate steps: detection and estimation. In the detection step, fluorophores are identified. In the estimation step, the locations of the identified fluorophores are estimated through an iterative approach. Here, we propose a non-iterative state space-based localization method which combines the detection and estimation steps. We demonstrate that the estimated locations obtained from the proposed method can be used as initial conditions in an estimation routine to potentially obtain improved location estimates. The proposed 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. The locations of the poles of the resulting system determine the peak locations in the frequency domain, and the locations of the most significant peaks correspond to the single molecule locations in the original image. The performance of the method is validated using both simulated and experimental data.


(000.5490) Probability theory, stochastic processes, and statistics; (100.2960) Image analysis; (100.6640) Superresolution; (110.3010) Image reconstruction techniques; (170.2520) Fluorescence microscopy

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