Self-Adaptive Mixed-Emitter Single-Molecule Localization Algorithm

Objective Currently, various super -resolution imaging technologies can surpass the Abbe diffraction limit, thereby improving imaging resolution to several tens of nanometers. This provides biologists with an effective tool for investigating biological structures and their functions on a novel scale. Among these, single -molecule localization techniques such as photoactivated localization microscopy (PALM) and stochastic optical reconstruction microscopy (STORM) yield the highest resolution. Traditional fitting -based methods, such as single -emitter localization (SE) and multi -emitter localization (ME) algorithms, employ fixed -size sliding windows to select the fitting areas. However, this was found to lead to an inadequate use of the prior emitter recognition information during the emitter localization stage in this study, thereby resulting in diverse advantageous density ranges and different artifact forms of SE and SM. The SE results are distorted by truncates near the emitters, which are generated by the fixed sizes of the fitting areas, whereas the ME suffers from an inappropriate fitting number. In summary, a self -adaptive mixed -emitter single -molecule localization algorithm (SM) that can adaptively determine the fitting area and fitting number is proposed in this study. Consequently, compared with the SE and ME algorithms, the images reconstructed by the SM algorithm exhibit a superior resolution and contrast over the complete density range on both simulated and experimental data.Methods The complete SM algorithm comprises several steps. First, an SNR binary map that can shrink and expand with the power of noise was generated based on the original image. Subsequently, the SNR binary map was combined with the local maxima for emitter recognition, and the sliding window and fitting number were generated using the SNR binary map. The center and size of the generated sliding window were then determined based on the center position and size of the connected domain, respectively, whereas the fitting number was obtained from previous emitter recognition results. Subsequently, maximum likelihood estimation (MLE) or least squares (LS) fitting was performed in each fitting area to obtain the subpixel positions. Finally, the performance of the SM algorithm was investigated using simulated and experimental data.Results and Discussions Under a low or high labeling density, the SM algorithm can effectively reduce crosstalk and mismatch errors, which promotes the recovery of super -resolution images closer to the synthesized benchmark images compared to those recovered by the SE and ME algorithms (Fig. 1). For a low labeling density, the SM algorithm exhibits a slightly better precision, recall, Jaccard index, and RMSE than the SE algorithm, and significantly superior results compared to those of the ME algorithm. With an increasing labeling density, the SM algorithm is marginally inferior to the ME algorithm in terms of the precision, recall, and Jaccard index, but is still significantly better than those of the SE algorithm. In terms of the RMSE, the SM and SE algorithms exhibit comparable localization errors, which are both worse than those of the ME algorithm [Figs. 3(a) -(c)]. Quantitative comparisons between the synthesized benchmark images and super -resolution images recovered by the different algorithms are performed using three indicators: PSNR, SSIM, and RMSE. The SM algorithm produces images with a higher similarity to the ground truth, as indicated by all three indicators (Table 1). In addition, it also successfully restores the structure with an interval of 20 nm, which is not achieved using the SE and ME algorithms [Figs. 3(d)-(e)]. On the alpha-tubulin dataset labeled as Alexa Fluor 647, the SM algorithm outperforms both the SE and ME algorithms in terms of resolution and contrast, as calculated using the FRC metrics (Fig. 4 and Table 2).Conclusions In this study, a self -adaptive mixed -emitter single -molecule localization algorithm that enables the adaptive determination of the fitting area and fitting number is proposed. Compared to the SE and ME algorithms, the SM algorithm can significantly reduce the artifacts caused by mismatch and crosstalk errors, resulting in an enhanced resolution and contrast within the full applicable density range of the fitting method. In terms of the speed, the current SM algorithm is faster than ME algorithm by a factor of 3-4, and slower than the SE algorithm by one order of magnitude. However, the number of fitting iterations required by the SM algorithm is the same as that required by the SE algorithm. Therefore, after optimization, the SM algorithm has the potential to achieve a speed comparable to that of the SE algorithm. Although the analysis and experiments in this study were conducted under two-dimensional and single -channel conditions, the inherent mechanism of the SM method allows for its easy integration with more complex single -molecule imaging technologies, such as three-dimensional and multi -channel situations. In future research, the SM algorithm should be further refined and its reliability and stability should be verified, thereby expanding its advantages in the field of biological imaging.