Abstract
Localization-based super-resolution microscopy (or called localization microscopy) rely on repeated imaging and localization of active molecules, and the spatial resolution enhancement of localization microscopy is built upon the sacrifice of its temporal resolution. Developing algorithms for high-density localization of active molecules is a promising approach to increase the speed of localization microscopy. Here we present a new algorithm called SSM_BIC for such purpose. The SSM_BIC combines the advantages of the Structured Sparse Model (SSM) and the Bayesian Information Criterion (BIC). Through simulation and experimental studies, we evaluate systematically the performance between the SSM_BIC and the conventional Sparse algorithm in high-density localization of active molecules. We show that the SSM_BIC is superior in processing single molecule images with weak signal embedded in strong background.
Highlights
A series of breakthroughs in far-field optical microscopy have been made, which dramatically improve the spatial resolution of conventional fluorescence microscopy by over an order of magnitude in both lateral and axial directions [1,2]
This algorithm, called SSM_BIC for the combination use of the Structured Sparse Model [11] and the Bayesian Information Criterion [12], exploits the fact that the number of active molecules in an image with low SBR could be reasonably estimated with high robustness by the Structured Sparse Model (SSM), which has become a major research field in signal processing for sparse image representation, and that a high probability for obtaining an optimal model for describing a low SBR image can be achieved with the Bayesian Information Criterion (BIC), a well-known criterion for model selection with the power of balancing training error and model complexity
The false-positive rate is defined as the ratio of false-positive positions to suspected positions found by the localization algorithm
Summary
A series of breakthroughs in far-field optical microscopy have been made, which dramatically improve the spatial resolution of conventional fluorescence microscopy by over an order of magnitude in both lateral and axial directions [1,2]. A final super-resolution fluorescence image could be obtained through repeating this cycle with typically many thousands of times, which depends mainly on the total number of active molecules necessary to be found within a diffraction limited area (or called Airy disk) for a desired spatial resolution [6] It is well-known that the high spatial resolution of localization microscopy is built upon the sacrifice of its temporal resolution. While at the same time, Huang et al applied multiple-emitter fitting and graphics processing unit (GPU) computation for fast and high precision localization of active molecules with high density [10] These algorithms were developed for single molecule images with very weak fluorescence background, which was calculated to have signal-background-ratio (SBR) of 3-10 and is not obtained from localization microscopy experiments (especially for those without TIRF illumination). This algorithm, called SSM_BIC for the combination use of the Structured Sparse Model [11] and the Bayesian Information Criterion [12], exploits the fact that the number of active molecules in an image with low SBR could be reasonably estimated with high robustness by the Structured Sparse Model (SSM), which has become a major research field in signal processing for sparse image representation, and that a high probability for obtaining an optimal model for describing a low SBR image can be achieved with the Bayesian Information Criterion (BIC), a well-known criterion for model selection with the power of balancing training error and model complexity
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