A variety of recent imaging techniques are able to beat the diffraction limitin fluorescence microcopy by activating and localizing subsets of thefluorescent molecules in the specimen, and repeating this process until all ofthe molecules have been imaged. In these techniques there is a tradeoff betweenspeed (activating more molecules per imaging cycle) and error rates (activatingmore molecules risks producing overlapping images that hide information onmolecular positions), and so intelligent image-processing approaches are neededto identify and reject overlapping images. We introduce here a formalism fordefining error rates, derive a general relationship between error rates, imageacquisition rates, and the performance characteristics of the image processingalgorithms, and show that there is a minimum acquisition time irrespective ofalgorithm performance. We also consider algorithms that can infer molecularpositions from images of overlapping blurs, and derive the dependence of theminimimum acquisition time on algorithm performance.
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