Super-resolution microscopy, such as stimulated emission depletion (STED) microscopy [1] and structured illumination microscopy (SIM) [2], delivers super-resolution imaging by modulating the illumination beams, while single-molecule localization microscopy (SMLM), including stochastic optical reconstruction microscopy (STORM) [3], photoactivated localization microscopy (PALM), and points accumulation for imaging in nanoscale topography (PAINT), exploits the fluorescent on/off properties of suitable organic dyes and fluorescent proteins to detect single molecules at different time points. In the cases where high-density fluorescent emitters are present in SMLM, common localization algorithms may fail to precisely localize single molecules, and thereby generate significant artifacts. Alternatively, fluorescence fluctuations super-resolution microscopy (FF-SRM) is a good candidate to address this issue by exploiting the random, independent, and uncorrelated nature of fluorescence intensity fluctuations over time. FF-SRM includes, e.g., super-resolution optical fluctuation imaging (SOFI), Bayesian analysis of blinking and bleaching (3B), multiple signal classification (MUSIC), and super-resolution radial fluctuations (SRRF) microscopy. SRRF processes raw fluorescence fluctuation images in both spatial and temporal domains. In the spatial domain, the average distance to lines of gradient around a point is measured [Fig. 1(b)] [4], representing the degree of convergence of the gradient. The mean convergence from the point (x_c, y_c) to the gradient line through the point (x_i′, y_i′) for the N ring coordinates is calculated to give the radiality of the pixel (x, y) in frame t,

 

Fig. 1. Super-resolution radial fluctuation microscopy image reconstruction algorithm schematic. (a) Raw image sequence and wide-field image of microtubules. (b) SRRF reconstruction steps. (c) VRRF reconstruction steps. The reconstruction is then completed using the SRRF algorithm. (d) eSRRF reconstruction steps. The VeSRRF algorithm first processes the image sequence through VRRF and then completes the image reconstruction using the eSRRF algorithm.

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An enhanced version of SRRF, namely enhanced-SRRF (eSRRF) [5], incorporates three key modifications to the original algorithm to improve image fidelity. Firstly, Fourier transform interpolation is deployed to generate subpixels, minimizing macro-pixel artifacts. Secondly, the calculation of mean convergence now employs radial gradient convergence (RGC) with a weighted factor map based on the user-defined radius R, i.e. the point spread function (PSF) size, and the intensity gradient of each pixel in the raw images. The RGC in the pixel (i₀, j₀) is

In a different approach, the intensity and gradient variance reweighted radial fluctuations (VRRF) [7] were independently developed to improve the imaging resolution and fidelity obtained by SRRF. As the temporal variance of intensity and gradient of a fluorophore contains its location estimation, VRRF quantitatively establishes the model of intensity and gradient fluctuations as the function of fluorophores’ locations. If the image of a sample is composed of the detections of N fluorophores, the intensity distribution at the location r over time tis

In this study, we introduce the VeSRRF algorithm for FF-SRM (Fig. 1). The method begins by utilizing the VRRF statistical variance analysis to perform an initial analysis on the fluorescence fluctuation image sequences. Thus the overlapping fluorescent molecules are separated, and the artifacts caused by the high-density fluorophores can be reduced. Subsequently, the processed image sequences are further analyzed in the eSRRF algorithm. By integrating the variance analysis of VRRF and eSRRF reconstruction, the VeSRRF algorithm can generate reconstructed images with optimal resolution and fidelity as the final outputs, outperforming other algorithms such as SRRF, VRRF/SRRF (referred to as VRRF for simplicity hereinafter), and eSRRF.

To quantitatively evaluate the quality of the reconstructed images produced by these algorithms, we utilized the open-source software ImageJ plugin NanoJ-SQUIRREL to analyze their resolution and fidelity. Within the software package, the functionalities of Fourier ring correlation (FRC) [8] resolution mapping and error mapping were implemented. FRC is a straightforward and objective method to measure the effective image resolution in localization microscopy. To calculate it, the image sequences were divided into two sub-groups containing the odd and even frames, and then the reconstructed super-resolution images from the two sub-groups were cross-correlated and plotted as a function of spatial frequency. The resolution of the image was determined at the frequency where the FRC curve drops to a value of 1/7. Error mapping was used to map the difference between a reconstructed super-resolution image and a reference image, i.e. a diffraction-limited wide-field image, at each pixel by calculating the resolution-scaled error (RSE) and resolution-scaled Pearson correlation coefficient (RSP) [6]. RSE is a metric of the root mean square error between the resolution-scaled image and the reference image. The lower value indicates better consistency. RSP is a dimensionless quantity ranging from −1 to 1. A higher value indicates better structural consistency between the resolution-scaled image and its reference image. Since we aimed at finding the algorithm reaching the best and most balanced resolution and fidelity, we adopted evaluation metrics QnR [5], as defined in the following equation,

Two simulated and five experimental datasets were used to evaluate the performance of the algorithms (Supplement 1 Methods A). Firstly, the simulated STORM dataset was from the SMLM Grand Challenge [9]. Secondly, the simulated dataset of fluorescence fluctuations was generated using the SuReSim software tool that simulates localization data from ground truth models [10]. Compared to other algorithms, the VeSRRF algorithm demonstrated outstanding performance in reconstructing fine structures and preserving fidelity in the simulated datasets (see Supplement 1 Figs. S1 and S2 for details).

STORM datasets of immunolabeled microtubules in fixed COS7 cells were tested in STORM, SRRF, eSRRF, VRRF, and VeSRRF. Both Tubulin-CF568 and Tubulin-AF647 in COS7 cells were imaged in a ZEISS Elyra PS.1 microscope under standard STORM imaging conditions. In Fig. 2, the diffraction-limited wide-field image [Fig. 2(a)] of Tubulin-CF568 in COS7 cells is shown with the corresponding super-resolution images from STORM, SRRF, eSRRF, VRRF, and VeSRRF algorithms [Fig. 2(b)–2(f), Supplement 1 Methods B1–4 and Tables S1–S3]. The enlarged views of a region of interest are displayed in the upper right corners of each image, from which it is evident that eSRRF preserved more structural information compared to that of VRRF but suffered lower resolution. The VRRF reconstruction produced a clearer recovery of fine structural information but may have generated over-sharpened microtubule artifacts. In contrast, the VeSRRF reconstruction achieved a good balance between the image resolution and fidelity, showing the fine structures of the microtubules in a practicable way. Spatial resolution was quantitatively compared using the FRC maps as shown in Figs. 2(g)–2(k), and the FRC values confirmed that VeSRRF reached the highest resolution obtained among the tested algorithms. The image fidelity was evaluated by calculating the error mapping values between the original wide-filed image and the reconstructed images, as shown in Figs. 2(l)–2(p). VeSRRF exhibited a high RSP value, demonstrating its ability to effectively preserve the structural information in the cell samples. Finally, the quantitative QnR assessment confirmed that VeSRRF achieved optimal performance in both resolution and fidelity, resulting in the highest QnR value (see Table. 1). The results of Tubulin-AF647 in COS7 cells were consistent with our previous findings (see Supplement 1 Fig. S3 for details). The experiment and tests showed that VeSRRF effectively super-resolved the cellular microtubule networks from STORM datasets while minimizing the artifacts regardless of the photoswitching properties of different types of dye molecules.

 

Fig. 2. Comparison of the reconstructed images of Tubulin-CF568 in fixed COS7 cells. (a) Wide-field image. (b)–(f) Reconstructed images from STORM, SRRF, eSRRF, VRRF, and VeSRRF algorithms. (g)–(k) Corresponding FRC maps. (l)–(p) Corresponding error maps. Scale bar in the enlarged image of the region indicated by the yellow border box: 1 µm.

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Table 1. FRC, RSP, and QnR Metrics in the Evaluation of the Quality of the Reconstructed Images From SRRF, eSRRF, VRRF, and VeSRRF

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Furthermore, fluorescence fluctuation image series obtained under a variety of signal-to-noise ratio (SNR) conditions were also tested in SRRF, eSRRF, VRRF, and VeSRRF. The first dataset of Tubulin-AF488 in fixed COS7 cells was acquired using a Mercury lamp illuminator in a ZEISS microscope. The second dataset of Tubulin-FLIP565 in fixed COS7 cells and the third dataset of Tubulin-QD800 in fixed HeLa cells were obtained from published papers [11,12], respectively. In Fig. 3, super-resolution images of Tubulin-AF488 in COS7 cells are shown (Supplement 1 Methods B1–3 and Tables S1–S3). From the enlarged region of interest, it was observed that the reconstructed image from VRRF showed some broken microtubule structures due to the nonlinear artifacts [Fig. 3(d)], which was also confirmed by the lower error mapping values from the RSP analysis [Fig. 3(l)]. Next, eSRRF gave a higher RSP value but lower resolution, as depicted in Figs. 3(g) and 3(k). In contrast, the reconstructed image from VeSRRF achieved the highest resolution and good fidelity, as shown in Figs. 3(i) and 3(m). Finally, the quantitative QnR assessment confirmed that VeSRRF achieved optimal performance considering both resolution and fidelity, resulting in the highest QnR value (see Table. 1). The results of Tubulin-FLIP565 in fixed COS7 cells and Tubulin-QD800 in fixed HeLa cells were consistent with our previous findings (see Supplement 1 Figs. S4 and S5 for details). The experiment and tests showed that VeSRRF effectively super-resolved the cellular microtubule networks from fluorescence fluctuation imaging while minimizing the artifacts under conditions of high-density fluorophores.

 

Fig. 3. Comparison of the reconstructed images of Tubulin-AF488 in fixed COS7 cells. (a) Wide-field images. (b)–(e) Reconstructed images from SRRF, eSRRF, VRRF, and VeSRRF algorithms. (f)–(i) Corresponding FRC maps. (j)–(m) Corresponding error maps. Scale bar in the enlarged image of the region indicated by the yellow border box: 2 µm.

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In summary, for each dataset, we calculated the FRC, RSP, and QnR values of the super-resolution images from SRRF, eSRRF, VRRF, and VeSRRF algorithms, and we compiled the results in Table 1. The eSRRF algorithm demonstrated better noise reduction and preservation of fine biological features. Its main improvement lies in the effective elimination of noise in temporal data, enhancing the SNR, and thus achieving more accurate image reconstruction. Compared to the original SRRF algorithm, the eSRRF algorithm can improve both image fidelity and resolution, although it still has certain limitations in resolution enhancement. Compared with the SRRF and eSRRF algorithms, VRRF can improve the resolution and contrast of the reconstructed images. However, the reconstructed images may exhibit artifacts and nonlinearities.

We found that the reconstruction algorithm combining VRRF and eSRRF, i.e. VeSRRF, can overcome the disadvantage of the lack of resolution or fidelity in SRRF, VRRF, and eSRRF. In our quantitative image quality analysis, the reconstructions from VeSRRF obtained the highest QnR values in both STORM and SRRF microscopy datasets, demonstrating its ability to achieve the optimal resolution and fidelity. Despite the outstanding performance of the VeSRRF algorithm in super-resolution microscopy, it is important to be aware of its limitations. Firstly, the selection of image reconstruction parameters has a significant impact on the quality of reconstructed images. To achieve the optimal image quality using VeSRRF, it is necessary to choose the appropriate combination of radius R and sensitivity S (Supplement 1 B2 and Table S3). To facilitate a simpler implementation, deep-learning-based data-driven optimization of input parameters will be investigated in future work. Secondly, achieving real-time image reconstruction is essential for applications such as live cell imaging or intraoperative pathological assessment. Therefore, there is a need to improve the run time of the VeSRRF algorithm (Supplement 1 Methods B6). Finally, microtubules in mammalian cells were chosen as the standard biological model system in this study. To give a comprehensive evaluation of the performance and applicability of VeSRRF, further testing of biological datasets featuring various cellular structures should be considered in future work. This will ensure that the VeSRRF algorithm is suitable for super-resolution microscopy of a broad spectrum of biological and medical specimens for optimal resolution and fidelity.

In this Letter, we developed a novel combinatory computational super-resolution microscopy method, namely VeSRRF, that demonstrated superior performance in STORM and SRRF microscopy. We performed super-resolution image reconstructions of the simulated and experimental datasets of cellular microtubule networks under sparse and dense fluorophore conditions and quantitatively evaluated and compared the super-resolution image quality in SRRF, eSRRF, VRRF, and VeSRRF using the FRC, RSP, and QnR metrics. Our results demonstrated that VeSRRF, the integrated VRRF, and eSRRF algorithms, not only achieved the highest resolution but also produced high fidelity in the reconstructed images, outperforming other algorithms in our tests. VeSRRF conveys super-resolution, high-fidelity biological imaging using standard, inexpensive optical microscopes, common fluorophores, and simple sample preparations, making it widely applicable to any life science laboratory. VeSRRF is an exemplary method in which complementary microscopy techniques are integrated holistically, creating superior imaging performance and capabilities. We anticipate that VeSRRF will emerge as a valuable tool for many researchers to simplify the quest to solve numerous complex biological problems.