Achieving increased resolution and reconstructed image quality with gradient variance modied superresolution radial uctuations

22 Based on the calculation of the degree of gradient convergence, the super- 23 resolution radial fluctuations (SRRF) algorithm can achieve higher resolution by 24 combining temporal fluctuation analysis with localization microscopy methods. The 25 algorithm is also capable of processing high-density fluorescence images. However, 26 there are considerable artifacts due to high density, which lead to a loss of image 27 resolution and low fidelity of images. This study demonstrates the use of fluorescence 28 gradient fluctuations in super-resolution analysis and proposes gradient variance 29 modified SRRF (gmSRRF) algorithm. The gmSRRF algorithm resolves finer structures 30 and compensates for the loss of resolution caused by artifacts in SRRF images using 31 relatively high-density stochastic optical reconstruction microscopy (STORM) data and


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In the last two decades, optical super-resolution imaging techniques have made 39 rapid and significant progress. The theoretical diffraction limit has been overcome using  16 . 3B can reach a resolution of ~50 nm, but 56 requires a large amount of calculation. For example, 6 h were required to analyze a 1.5 57 × 1.5 μm region 14 . SOFI can achieve a resolution of ~150 nm, but requires thousands 58 of frames. Although SRRF has achieved approximately 105 nm for widefield and 80-59 98 nm for confocal microscopy data using hundreds of slides or less 16 , high-density 60 fluorescence signals will cause artifacts and decrease the actual resolution of the SRRF 61 images. 62 Here, we present a gradient variance modified SRRF algorithm (gmSRRF) that 63 addresses artifacts by combining SRRF with the temporal statistics analysis of intensity 64 and gradient fluctuations. The optimization algorithm was verified using stimulated and 65 experimental data. Compared with the SRRF algorithm, the gmSRRF algorithm was 66 proven to achieve better super-resolution reconstructed images with fewer artifacts 67 caused by high density and background noise. Additionally, it was applicable to 68 widefield and confocal data. There is a conflict between the density of activated fluorophores per frame and the 72 necessary number of frames needed to reconstruct a complete image. SMLM requires 73 low density data for high precision localization, so many frames are needed. SRRF is a 74 super-resolution algorithm that does not depend on the sparse distribution of excited 75 fluorophores 17 . Thus, it can achieve super-resolution with fewer frames than SMLM. It 76 calculates the degree of local gradient convergence (radiality) of an image sequence 77 and combines the radiality stack into one reconstructed image through temporal 78 analysis on a sub-pixel scale 18 . SRRF also interpolates the images by a factor of 79 "magnification" before processing. However, for high-density data in areas where 80 structures are close and complex, two or more fluorophores can overlap so that the 81 calculated radiality stack cannot achieve multi-center of radiality. This results in 82 artifacts or even misinterpretation of biological structures in reconstructed images, as 83 shown at the bottom of Fig. 1a. These artifacts cannot be depressed by increasing the 84 number of frames. Fewer frames are necessary to compose a super-resolution image 85 using SRRF if artifacts produced during the processing of high-density data are reduced.

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Modifying raw data is a feasible way to erase artifacts in SRRF images.

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Temporally dynamic pixel values in a sequence of fluorescence images contain two 88 major parameters of labeled structures, intensity and gradient, denoted by U(r,t) and    The intensity distribution function is expressed as: where U(r) is the point spread function, ai is the maximum brightness of the 120 fluorophores, and fi(t) is the blinking function, assumed to stochastically range between 121 0 and 1.

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Variance is used as a quantitative indicator to describe the time-varying properties of 123 G(r,t) and U(r,t). Here, the variance is equivalent to the concept of zero-time lag 124 second-order auto-cumulant 21 . The intensity variance is expressed as: 129 Subsequently, we use a Gaussian PSF, and the gradients can be expressed as: Following the same simplification method, gradient variance can then be expressed as:  nm, simple SRRF reconstruction processing caused many artifacts, as shown in Fig. 2d.

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At the same time, the profile of the intensity section also revealed an unveracious peak 172 between the double-lines, as seen in Fig. 2e. In contrast, the gmSRRF algorithm reduced 173 artifacts and maintained high fidelity and higher resolution of the reconstructed images. The gmSRRF algorithm was tested on images from high-density STORM data to 186 verify the practical effectiveness of reducing artifacts originating from high density.

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The algorithm was also applied to widefield, confocal, and SIM data to research the 188 scale of applicability. for the temporal analysis, which was the temporal radiality average.