Abstract
Super-resolution optical fluctuation imaging (SOFI) offers a simple and affordable alternative to other super-resolution (SR) imaging techniques. The theoretical resolution enhancement of SOFI scales linearly with the order of cumulants, while the imaging conditions exhibit less photo-toxicity to the living samples as compared to other SR methods. High order SOFI could, therefore, be a method of choice for dynamic live cell imaging. However, due to the cusp-artifacts and dynamic range expansion of pixel intensities, this promise has not been materialized as of yet. Here we investigated and compared high order moments vs. high order cumulant SOFI reconstructions. We demonstrate that even-order moments reconstructions are intrinsically free of cusp artifacts, allowing for a subsequent deconvolution operation to be performed, hence enhancing the resolution even further. High order moments reconstruction performance was examined for various (simulated) conditions and applied to (experimental) imaging of QD labeled microtubules in fixed cells, and actin stress fiber dynamics in live cells.
Highlights
Fluorescence microscopy is widely utilized in biological studies due to its high sensitivity and specificity
A concluding discussion is given in section 6, summarizing our main findings: (I) even-order moments reconstruction is intrinsically free of cusp artifacts; (II) it can be independently combined with deconvolution without conflicting with the commonly used positivity constraint in image deconvolution; and (III) application of ldrc can correct for the expanded dynamic range of pixel intensities
Inspired by the interchangeable relation between cumulant and moment [35], we investigated the statistical behavior of high-order moments of emitter blinking trajectories expressed as a function of the ‘on time ratio’ in a similar way to cumulant analysis [33]
Summary
Fluorescence microscopy is widely utilized in biological studies due to its high sensitivity and specificity. A concluding discussion is given, summarizing our main findings: (I) even-order moments reconstruction is intrinsically free of cusp artifacts; (II) it can be independently combined with deconvolution without conflicting with the commonly used positivity constraint in image deconvolution; and (III) application of ldrc can correct for the expanded dynamic range of pixel intensities. Under the framework of virtual emitter interpretation [33], the physical meaning of the joint-cumulant calculated for a set of pixels (either with or without pixel repetition) is taken to mean as the image formed by virtual emitters at the locations of the original emitters, but having virtual brightnesses These virtual brightnesses are the products of εn (meaning the nth power of the original ‘on-state’ brightness of the emitter) and wn( bk(t)) (meaning the nth order cumulant of the blinking profile of the corresponding emitter with the time lags defined for the overall joint-cumulant function). Since images are usually presented with positive pixel values, the absolute value operator could yield an image with cusp-artifacts, degrading the image quality of highorder SOFI cumulants [33]
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