Objective Although the acquisition of single-molecule localization microscopy (SMLM) includes various noises and background information, completely removal of structural noise is difficult for current denoising algorithms (e.g., the spatial wavelet algorithm and the extreme value-based emitter recovery algorithm) employed in the preprocessing of the reconstruction, thus decreasing the quality of reconstructed super-resolution images. To address this challenge, we develop a new background denoising algorithm based on the time-domain iterative wavelet transform (TDIWT), which can process a batch of SMLM datasets with different signal-to-noise ratios (SNRs) by adaptively selecting the appropriate levels and iterations. This algorithm can provide a new approach for adaptive batching SMLM data structural background.
Methods This denoising algorithm based on TDIWT includes two main parts. First, the appropriate level and iteration parameters of TDIWT are adaptively selected for different datasets to balance the time consumption and signal-noise separation effects by calculating the SNR of the dataset. Consequently, time-varied values of each pixel are calculated using TDIWT with selected parameters to separate the signal and background structural noise. The main steps of TDIWT calculation are described by (1) extracting the intensity of the signal from each pixel in a stack in the time domain; (2) acquiring the approximate coefficient via wavelet decomposition and then using it for wavelet reconstruction to fit the background curve; (3) estimating the reconstructed signal that is higher than the background curve and employing wavelet decomposition again; (4) repeating the process until the background fitting data is acquired; (5) outputting separated signal and background image according to the image size (Fig. 1).
Results and Discussions The simulated results demonstrate that the separation of signal and background using the TDIWT algorithm is more efficient than that using the other denoising algorithms (i.e., extreme value-based emitter recovery, Gaussian filter, background estimation based wavelet transform, median filter, and rolling filter) by evaluating the direct visualization and the quantitative parameters including structural similarity index measure (SSIM) and peak signal-to-noise ratio (PSNR), as shown in Figs. 3 and 4. The SSIM and PSNR of the TDIWT algorithm are 29.9%, 68.5%, 226%, and 33.3%, 34%, 50.8% higher than that of the spatial wavelet algorithm (i.e., background estimation based wavelet transform) using SNR10, SNR6, and SNR2 datasets, respectively. This can be explained by the fact that the intensity of the signal varies rapidly, but the background structural noise varies gradually in the time domain. This advantage of the TDIWT algorithm is more noticeable under the low SNR with a strong structural background. The normalized intensity of signal near strong structural noise is calculated, as shown in Fig. 3, illustrating that the separated signal using the TDIWT algorithm is the closest to the simulated signal compared with the other algorithms and demonstrating the improved accuracy of signal extraction. In addition, the experimental data acquired using our easySTORM system and the real reference data from an open single-molecule localization website are employed to further evaluate the developed algorithms. The reconstructed tubulin images show a continuous state using the TDIWT algorithm and a discontinuous state using the other algorithms from the same dataset with strong structural noise, as shown in Fig. 5. Figure 7 also demonstrates that the TDIWT algorithm could more effectively remove the structural noise.
Conclusions In this study, we have developed a new denoising algorithm based on a time-domain iterative wavelet algorithm, which can process a batch of SMLM datasets with different SNRs by adaptively selecting the appropriate levels and iterations. This algorithm can provide an accurate signal extraction from the noisy background, thus improving super-resolution image reconstruction. Under the simulation datasets, the results have demonstrated that the structural similarity index and peak SNR of processed datasets using the TDIWT algorithm are increased by 226%, 50.8%, and 58.5%, 16.6% compared with that using the spatial wavelet and time extremum emitter recovery algorithm, respectively. In addition, the experimental data acquired using our easySTORM system and the data from the open single-molecule localization website have been employed to evaluate the algorithms. The reconstructed tubulin images have shown a continuous state using the TDIWT algorithm and a discontinuous state using the other algorithms from the same dataset, verifying the superiority of the algorithm. This denoising algorithm based on TDIWT can provide a new approach for adaptive batching SMLM data structural background.
