Abstract
Structured illumination can reject out-of-focus signal from a sample, enabling high-speed and high-contrast imaging over large areas with widefield detection optics. However, this optical sectioning technique is currently limited by image reconstruction artefacts and poor performance at low signal-to-noise ratios. We combine multicolour interferometric pattern generation with machine learning to achieve high-contrast, real-time reconstruction of image data that is robust to background noise and sample motion. We validate the method in silico and demonstrate imaging of diverse specimens, from fixed and live biological samples to synthetic biosystems, reconstructing data live at 11 Hz across a 44 × 44μm2 field of view, and demonstrate image acquisition speeds exceeding 154 Hz.
Published by Optica Publishing Group under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
1. Introduction
Widefield fluorescence microscopy permits the imaging of biological structures with a high specificity, however, out-of-focus light limits image contrast. Unless planar excitation profiles are used for illumination – such as in lightsheet [1] or HiLo [2] microscopy – fluorescent probes located above and below the focal plane contribute to the signal collected in the final image.
Scanning confocal microscopy circumvents this problem through the use of a pinhole to physically reject out-of-focus signal. While this is effective at increasing contrast, only a single point in the sample can be imaged at a time and images must be built up sequentially, pixel-by-pixel, greatly increasing acquisition time. Furthermore, high excitation powers are required to compensate for the signal lost through the pinhole.
A different approach to achieve optical sectioning (OS) is through structured illumination microscopy (SIM) [3]. Here, a fluorescent sample is illuminated by patterned excitation light and the emitted fluorescence is imaged with widefield detection. In super-resolution (SR) SIM, interference patterns are produced by the interaction of the patterned excitation with the structures of the sample and these interference patterns are used to extract high-resolution information about the sample [4,5]. OS-SIM makes use of the fact that the modulation depth of the excitation pattern is highest in the in-focus plane and decreases rapidly with distance from it. Hence, the in- and out-of-focus structures can be distinguished by differences in stripe contrast. To achieve this, the sample is typically illuminated with a sinusoidal stripe pattern, and three sequential images are acquired as the pattern is shifted in phase over the sample. Under these conditions, only the in-focus structures will show a change in intensity between the phase shifted images and therefore these can be extracted and the three raw images reconstructed into one optically sectioned image. This method was pioneered by Neil et al. [3] who used the squared difference (SD) between the three phases to reconstruct the image:
where $I_R$ is the reconstructed image and $I_{n}$ represents the $n^{th}$ phase image of the sample under striped illumination with the phase shifted by $2(n-1) \pi$/3. Phase stepping in this way ensures a uniform average illumination and prevents striping artefacts in the reconstructed image. While simple to implement, this method is highly sensitive to noise, which becomes amplified in the SD reconstruction. Additionally, even small movements of the sample or deviations from the ideal phase step size introduce reconstruction artefacts. Later efforts improved on this early SD method, by compensating for small errors in pattern phase [6] and reducing artefacts at low signal-to-noise ratios with HiLo filtering [7]. However, reconstructions remain sensitive to noise and prone to artefacts.Since the early days of mechanically moved diffraction gratings, there have also been numerous developments in the techniques used to generate the sinusoidal patterned illumination. Currently, the most common techniques are based on digital micromirror devices (DMDs) [8] or liquid crystal spatial light modulators (SLMs) [9–11], with SLMs generally proving the more popular technology due to the improved light efficiency. When combined with suitable image denoising algorithms, the fast switching times of these devices have allowed for SR-SIM at speeds exceeding 180 Hz [12]. However, there are a number of limitations associated with these, including the complexity of the optical setup, the high cost of components with a sufficient optical flatness, and a field of view (FOV) that is limited by the physical size of the device.
Complications also arise when these methods are to be used for imaging in multiple colours. For optimal reconstructions of OS-SIM data, the spatial frequency of the striped illumination pattern must be half of the maximum spatial frequency observable by the microscope [3]. This resolution limit changes with wavelength, and since SLMs can only display a single pattern at a time, either colour channels must be imaged sequentially, or the user must accept a reduced performance. While the impact of using the same pattern for different wavelengths is less severe for OS-SIM than for SR-SIM, problems arise when a large range of wavelengths is required. In particular, the desired diffraction orders for the different colours become spatially separated to such an extent that using a mask to filter out spurious higher diffraction orders becomes challenging. When using liquid crystal SLMs, there are further limitations in the range of illumination wavelengths that can be used, as the diffraction efficiency drops rapidly outside of the designed centre wavelength and the devices themselves become damaged by high-power illumination with shorter wavelengths.
We address these issues by combining machine learning (ML) with interferometric pattern generation for OS. Our interferometric SIM method is low cost, simple to implement, and is ideally suited to high speed imaging of samples with a wide range of excitation wavelengths. We use two complementary neural networks to reconstruct OS-SIM data: a fast network for real-time reconstructions and a heavier network for post-acquisition reconstructions. Using the fast-reconstruction network, we demonstrate on-the-fly processing of OS-SIM data, allowing users to immediately and intuitively visualise reconstructions as they navigate the sample. We also demonstrate that by building sample motion into the image formation model, we remove the striping artefacts seen when imaging highly dynamic samples. The software to achieve these reconstructions is packaged in a user-friendly graphical user interface (GUI) which makes the method immediately applicable to both new and existing OS-SIM setups.
2. Methods
2.1 Hardware implementation
To overcome the issues associated with SLMs and DMDs, we use an interferometric method for pattern generation (Fig. 1) [13]. The setup makes use of a Michelson interferometer to produce the sinusoidal illumination, where phase stepping is achieved by laterally sweeping the pattern across the sample with a single galvanometric mirror element. In this way, the periodicity of the sinusoidal interference fringes depends on the wavelength of the excitation light, meaning the fringe spacing is optimised for all wavelengths simultaneously. Additionally, interference fringes can be generated for any wavelength supported by the beamsplitting element. In our setup, fluorescence signal from the sample is collected and split into three colours using an image splitting device, permitting the simultaneous imaging of multiple colour channels. A Python GUI enables hardware control and display of reconstructed images in real time (Fig. S3). All source code is available in a GitHub repository [14].
2.2 Subtractive reconstructions
In addition to the classical SD approach (Eq. (1)), we tested a corrected SD method (Eq. (2)) [6] and a filtered SD reconstruction algorithm by Li et al. (Eq. (3)) [7]. The corrected SD method compensates for uneven phase stepping of the pattern by weighting the components of the reconstruction according to the phase of the excitation pattern:
Based on the HiLo concept introduced by Lim et al. [16,17], the mixed filtering method further refines this corrected OS-SIM image by combining the high spatial frequency information from the predicted widefield image, with the low spatial frequency information from the OS-SIM image. The widefield image is high-pass (HP) filtered and mixed with the low-pass (LP) filtered OS-SIM image according to a weighting parameter $\alpha$:
This has the effect of simultaneously removing the out-of-focus light while making use of the widefield image to reduce the noise introduced by the SD-SIM reconstruction. The filter width is determined by the frequency of the fringe pattern and the mixing parameter, $\alpha$, is chosen based on the modulation depth of the pattern. Finally, the mixed filter method applies a stripe suppression filter to the reconstruction by attenuating the spatial frequencies in the image near to the spatial frequency of the excitation stripe pattern.
The basic, corrected and filtered SD reconstructions were calculated in MATLAB.
2.3 Machine learning reconstruction
Machine learning (ML) has become a powerful tool for the pre-processing, post-processing and reconstruction of SR-SIM data [20]. Compared to classical methods, ML can increase reconstruction quality and does not require the estimation of system parameters. For OS, ML has been used to generate sectioned images directly from widefield images [21]. By training a network on a sample-by-sample basis, learned a priori knowledge of the sample can be used to improve contrast, although this method is susceptible to sample variations and requires an existing optical sectioning system to provide the training data. ML has additionally been applied to the reconstruction of OS-SIM data [22], although the impacts of pattern phase error and sample movement have not been fully addressed. Here, we leverage recent advances in ML and optimise two distinct neural networks specifically for the reconstruction of interferometrically generated OS-SIM data. By using two networks, we are able to achieve real-time reconstructions at the point of acquisition, and high-fidelity reconstructions post-acquisition, yielding optimised results even for moving samples.
2.3.1 Residual channel attention network
In the first instance, ML-OS-SIM reconstructions were performed using a lightweight convolutional neural network (CNN) based on the residual channel attention network (RCAN) architecture [19,23]. This RCAN model has a low memory footprint and can perform reconstructions on low-end consumer graphics cards at rates compatible with live reconstruction during imaging. The network consisted of three groups of ten residual channel attention blocks (RCABs) each with 96 filters based on a 3 $\times$ 3 kernel (Fig. 2(C)). Unlike in previously reported implementations of the RCAN architecture for SIM, the initial "head" layer was adjusted to use learnable filters with a size of $7~\times ~7$.
2.3.2 Video super-resolution network
For high-fidelity image reconstruction post-acquisition, we use a video super-resolution (VSR) transformer network based on the shifted window architecture (Fig. 2) [18,24–27]. By using 3-dimensional patches, this VSR network is optimised to combine information from adjacent frames in a sequence acquisition, offering improved performance on moving structures. The multi-head self-attention mechanism of the Swin transformer is supplemented with a channel attention mechanism based on a single RCAB (Fig. 2(C)).
2.3.3 Data generation
To mitigate the challenges posed by training on experimentally acquired OS-SIM data, we simulated large datasets and employed transfer learning to train the network. This approach offers several advantages: firstly, for supervised learning, the ground truth is known, ensuring that the networks do not learn to generate the same artefacts produced by classical reconstruction algorithms. Secondly, large and diverse training datasets can be generated, enabling the models to learn the reconstruction process without overfitting to smaller experimental datasets. Thirdly, it is possible to train the network to be robust to the specific challenges associated with reconstructing interferometric OS-SIM data, particularly noise and sample motion.
Two separate datasets were generated for the network training with the datasets tailored for each network. For the RCAN model, where reconstruction speed requires a smaller network, the in-focus plane was simulated from a library of high-resolution static images. This aligns with the primary goal of the RCAN model: to provide the user with real-time reconstructions at the expense of robustness to the artefacts associated with moving samples. For the VSR network, these static OS-SIM data were supplemented with data simulating samples with moving structures. Here, the in-focus plane was generated from three sequential frames in video sequences from BBC nature documentaries, mimicking samples that move during acquisition. For both the VSR and RCAN training datasets, the structures of the out-of-focus planes of the sample were simulated by taking static images from the DIV2K dataset [28]. From these ground-truth images, model OS-SIM data were generated by multiplying both the in-focus and out-of-focus planes with a sinusoidal excitation pattern, and subsequently blurring them by convolution with either the in-focus or out-of-focus point spread functions (PSFs). The planes were then merged using a weighted addition. Varying levels of Gaussian and Poissonian noise were added to the raw frames after combination. The parameters for generating the PSFs and the excitation pattern were randomised, allowing the models to generalise to data collected on a range of microscopes and in varying imaging conditions.
2.3.4 Network training
Both networks were trained in Python using the Pytorch framework. The networks were trained on 5000 simulated images for 200 epochs on an Nvidia RTX3070 graphics card. For the VSR network, these 5000 simulated images were composed of 2000 static targets and 3000 moving targets. The networks were trained using the Adam optimiser. For the initial 100 epochs, the mean square error (MSE) loss function was used, which was changed to the L1 absolute difference loss function for the final 100 epochs. These loss functions were calculated relative to the high-resolution ground-truth in-focus image. For the VSR network, the second frame in the sequence was used to provide this ground truth. Under these conditions, network training took approximately 20 h for the RCAN model and 38 h for the VSR network.
3. Results and discussion
3.1 Machine learning improves contrast and minimises noise in optical sectioning
The models were initially validated by demonstrating their performance on simulated 3D samples comprising a mesh of filaments (Fig. 3). Simulated data were generated in MATLAB from an artificial ground truth by multiplying the mesh with a striped excitation pattern and convolving the fluorescent response with an ideal widefield PSF. The PSF was calculated using the Born and Wolf model for an emission wavelength of 600 nm, a water immersion objective lens with $NA = 1.2$, and voxels measuring $86~\times ~86~\times ~$ 86 nm$^3$. The recovery of lost axial information can be visualised in the Fourier transforms of the simulated and reconstructed data (Fig. 3). To measure the performance of the ML reconstructions in the presence of noise, a fixed level of Gaussian noise and varying levels of Poissonian noise were added to mimic imaging with low photon counts. Poissonian noise was modelled by sampling pixel values from a Poisson distribution scaled by $\eta ~\times ~10^{12}$, where lower values of $\eta$ correspond to fewer photons collected from the sample. Figure 4 shows a comparison of the ML and filtered SD reconstruction methods. The performance was further quantified by measuring the structural similarity between the ideal, noise-free, optically sectioned image and the reconstruction (Fig. 5). As expected, the fidelity of all reconstruction methods is reduced as noise is increased. However, ML reconstruction showed a lower sensitivity to noise, and VSR successfully reconstructed OS-SIM data with a fifth of the signal required for SD reconstruction.
3.2 Video transformer reconstruction removes motion artefacts from optical sectioning reconstructions
When using subtractive methods to determine variations in pattern contrast, it is vital that the sample does not move by more than the diffraction limit between pattern shifts. If this assumption is not satisfied, moving objects appear replicated and stripe artefacts are introduced into the final image. To measure the impact of sample movement on reconstruction quality, reconstruction methods were tested on data simulating OS-SIM imaging of structures that move between frames (Fig. 6(A),B). In the subtractive SD reconstruction, the moving structures produce the typical shadowing artefacts seen in OS-SIM imaging of highly dynamic samples (Fig. 6(C)). These artefacts, however, are effectively suppressed in the VSR reconstruction, which shows no shadowing or striping whilst still removing out-of-focus light from the images. This improved performance can be quantified by measuring the structural similarity between the reconstructions and an ideal image of the sample at a single timepoint during acquisition (Fig. 6(D)). This ideal ground truth was calculated from the second frame of the video data that was used to simulate the moving object (Fig. 6(B)). Averaged over 8 simulated images, the VSR method provided the most accurate and consistent reconstructions. It was observed that the increased variation in reconstruction quality seen with the other methods resulted from differences in the size and speed of the moving objects in the sequence, with reconstruction quality decreasing as movement in the sample increased. It should also be noted that, as with noisy data, the artefacts introduced by the subtractive methods can lead to reconstructions that show no quantitative improvement over widefield images, even if there is a qualitative improvement in image contrast.
3.3 Machine learning outperforms subtractive reconstruction on experimental optical sectioning data
Finally, the reconstruction methods were validated on experimental data by imaging the same sample with confocal and OS-SIM microscopy. The confocal image provides an ideal ground truth reference to determine the reliability of the reconstructed images (Fig. 7). As expected, all OS-SIM methods qualitatively showed a reduction in the out-of-focus signal. However, quantitative analysis of the reconstructions reveals that for the subtractive methods, the amplified noise significantly reduces the reliability of the reconstruction, indicating that at even modest noise levels, reconstructions are a worse representation of the underlying structure than the widefield image. In contrast, both ML methods provided improved contrast and a more accurate representation of the sample.
3.4 ML-OS-SIM can image faster than point scanning confocal microscopy with similar imaging performance
To demonstrate the speed improvement possible with interferometric ML-OS-SIM, the system was compared to point scanning confocal microscopy (Fig. 8). The camera exposure time was adjusted to produce reconstructions of a similar quality to confocal images of the same sample. In both images, background light is effectively removed and the 3D microtubule network of the cell can be resolved free from artefacts. However, ML-OS-SIM imaging was considerably faster: a 44 $\times$ 44 $\times$ 5 ${\mu }m^3$ volume could be imaged and the OS reconstruction presented to the user in < 2 s, whereas scanning confocal imaging took 2 min 36 s. That is, ML-OS-SIM was approximately 78 times faster. This speed advantage, in combination with the lower illumination laser power required, results in less photobleaching and photodamage to delicate samples (Supplement 1). An advantage of ML-OS-SIM is that a single detector can be used in conjunction with detection-splitting optics, whereas a confocal system would require an additional detector for each channel.
For single-colour imaging, live reconstruction data can be presented to the user at up to 11 Hz over the full FOV. Imaging can also be performed over smaller FOVs without live reconstruction when speed is important, enabling imaging speeds of 463 Hz over an 11 $\times$ 11 ${\mu }m^2$ FOV, equivalent to 154 reconstructed frames per second. We note that at smaller FOVs and with a sufficiently bright sample, imaging speeds exceeding 4.8 kHz would be possible with the current interferometric setup (Supplement 1).
3.5 ML-OS-SIM enables the volumetric imaging of structures in multiple colours
To demonstrate the capabilities of the technique for biological imaging, live cells were imaged in multiple colours across a 5 ${\mu }m$ axial range (Fig. 9). Figure 9(A) depicts a maximum intensity projection of the mitochondrial network of a live cell imaged at a snapshot in time where the colourmap indicates the depth within the cell. No movement or striping artefacts are discernible in the image. Furthermore, the multicolour capability of the system allows several structures to be visualised without a temporal delay between colour channels. Figure 9(B) shows a two-channel time series of projections from the volumetric data. Here, a lysosome (green) can be seen to push a mitochondrial structure (purple) out of the way as it is transported through the cell.
3.6 Multicolour 3D imaging of DNA-nanotechnology biomimetic behaviours with ML-OS-SIM
In addition to biological samples, the contrast enhancement afforded by our ML-OS-SIM strategy enables the visualisation of processes in synthetic cell science. Recently, the synergy between lipid-membrane phase behaviour and the tools of DNA nanotechnology has gained traction to engineer bio-inspired responses in cell-like objects [30,31]. Figure 10 shows ML-OS-SIM images of DNA nanostructures tethered to phase-separated lipid membranes. The fast ML-OS-SIM technique allows for the reconstruction of multicolour 3D views of DNA-functionalised giant vesicles that can sustain biomimetic cargo transport pathways across their membrane surface (Fig. 10) [29]. Chemical stimulus, in the form of DNA oligonucleotides, triggers the lateral re-organisation of DNA nanostructures, leading to the transport of fluorescently labelled DNA cargoes (blue), away from the liquid-disordered phase (yellow) to liquid-ordered lipid domains (Fig. S5). The responsive DNA nanostructures harness established strand displacement mechanisms [32,33] and the preferential tendency of different hydrophobic anchors in membrane-bound DNA to enrich distinct lipid domains [29]. The speed of ML-OS-SIM enables 3D imaging of the structures, allowing for better visualisation and understanding of the re-organisation process [29].
4. Conclusion
To date, OS-SIM has been simultaneously limited by a lack of robust reconstruction algorithms and limitations in the instrumentation used for pattern generation. Here, we demonstrate that ML reconstruction methods enable multicolour OS-SIM across a 44 $\times$ 44 ${\mu }m^2$ FOV, with the option to view real-time reconstructions at up to 11 Hz. The use of a shifted window transformer architecture makes our method immune to the reconstruction artefacts common in traditional, subtractive techniques.
Additionally, we demonstrate that the improved reconstruction methods are ideally combined with interferometric pattern generation. This method provides a simple and lower cost alternative to existing technologies based on SLMs. We achieve multi-label volumetric imaging, allowing for the interactions between structures to be visualised with no temporal lag. The interferometric pattern generation technique opens up the possibility of performing optical sectioning simultaneously over wavelength ranges spanning ultraviolet to far red with no changes to the optical setup. The widefield detection method employed by ML-OS-SIM means that optically sectioned images comparable to confocal microscopy can be achieved at speeds up to 154 Hz, reducing photodamage to the sample. These capabilities are typically only afforded by lightsheet imaging modalities, but at the cost of greatly increased system complexity and non-conventional imaging geometries.
Funding
Michael J. Fox Foundation for Parkinson's Research (022159, 16238); Alzheimer’s Research UK (ARUK-PG013-14); Royal Society (UF160152, URF\221009); H2020 European Research Council (ERC-STG No 851667 NANOCELL); Biotechnology and Biological Sciences Research Council (BB/X010228/1); Infinitus Ltd.; Medical Research Council (MR/K015850/1, MR/K02292X/1); Wellcome Trust (065807/Z/01/Z, 089703/Z/09/Z, 203249/Z/16/Z, 3-3249/Z/16/Z); Engineering and Physical Sciences Research Council (EP/H018301/1, EP/L015889/1, EP/S022139/1, EP/S023046/1).
Acknowledgments
The authors would like to thank Lisa Hecker for her help constructing the interferometric setup. C.F.K. acknowledges funding from the UK Engineering and Physical Sciences Research Council (EP/L015889/1 and EP/H018301/1), the Wellcome Trust (3-3249/Z/16/Z and 089703/Z/09/Z), the UK Medical Research Council (MR/K015850/1 and MR/K02292X/1), and Infinitus Ltd. R.R.S. acknowledges funding from the Biotechnology and Biological Sciences Research Council through a BBSRC Discovery Fellowship (BB/X010228/1). R.R.S. and L.D.M. acknowledge funding from the European Research Council (ERC) under the Horizon 2020 Research and Innovation Programme (ERC-STG No 851667 NANOCELL). L.D.M. acknowledges funding from a Royal Society University Research Fellowship (UF160152, URF$\backslash$R$\backslash$221009). G.S.K.S. acknowledges funding from the Wellcome Trust (065807/Z/01/Z) (203249/Z/16/Z), the UK Medical Research Council (MRC) (MR/K02292X/1), Alzheimer Research UK (ARUK) (ARUK-PG013-14), Michael J Fox Foundation (16238 and 022159), and Infinitus China Ltd. S.K. acknowledges funding from the UK Engineering and Physical Sciences Research Council (EPSRC) grant EP/S023046/1 for the Centre for Doctoral Training in Sensor Technologies for a Healthy and Sustainable Future. R.M.M. and J.R.L. acknowledge funding from the UK Engineering and Physical Sciences Research Council (EP/S022139/1).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented and the code used for image reconstruction and hardware control can be found at the GitHub repository [14].
Supplemental document
See Supplement 1 for supporting content.
References
1. J. Huisken, J. Swoger, D. Bene, et al., “Optical Sectioning Deep Inside Live Embryos by Selective Plane Illumination Microscopy,” Science 305(5686), 1007–1009 (2004). [CrossRef]
2. M. Tokunaga, N. Imamoto, and K. Sakata-Sogawa, “Highly inclined thin illumination enables clear single-molecule imaging in cells,” Nat. Methods 5(2), 159–161 (2008). [CrossRef]
3. M. A. A. Neil, R. Juškaitis, and T. Wilson, “Method of obtaining optical sectioning by using structured light in a conventional microscope,” Opt. Lett. 22(24), 1905–1907 (1997). [CrossRef]
4. R. Heintzmann and C. G. Cremer, “Laterally modulated excitation microscopy: improvement of resolution by using a diffraction grating,” in Optical Biopsies and Microscopic Techniques III, vol. 3568 (SPIE, 1999), pp. 185–196.
5. M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198(2), 82–87 (2000). [CrossRef]
6. M. J. Cole, J. Siegel, S. E. D. Webb, et al., “Time-domain whole-field fluorescence lifetime imaging with optical sectioning,” J. Microsc. 203(3), 246–257 (2001). [CrossRef]
7. Z. Li, Q. Zhang, S.-W. Chou, et al., “Fast widefield imaging of neuronal structure and function with optical sectioning in vivo,” Sci. Adv. 6(19), eaaz3870 (2020). [CrossRef]
8. T. Fukano and A. Miyawaki, “Whole-field fluorescence microscope with digital micromirror device: imaging of biological samples,” Appl. Opt. 42(19), 4119 (2003). [CrossRef]
9. P. Kner, B. B. Chhun, E. R. Griffis, et al., “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6(5), 339–342 (2009). [CrossRef]
10. L. J. Young, F. Ströhl, and C. F. Kaminski, “A guide to structured illumination TIRF microscopy at high speed with multiple colors,” J. Visualized Exp. 30(111), 53988 (2016). [CrossRef]
11. T. Zhao, H. Hao, Z. Wang, et al., “Multi-color structured illumination microscopy for live cell imaging based on the enhanced image recombination transform algorithm,” Biomed. Opt. Express 12(6), 3474 (2021). [CrossRef]
12. X. Huang, J. Fan, L. Li, et al., “Fast, long-term, super-resolution imaging with Hessian structured illumination microscopy,” Nat. Biotechnol. 36(5), 451–459 (2018). [CrossRef]
13. E. N. Ward, L. Hecker, C. N. Christensen, et al., “Machine learning assisted interferometric structured illumination microscopy for dynamic biological imaging,” Nat. Commun. 13(1), 7836 (2022). [CrossRef]
14. E. N. Ward, C. N. Christensen, and R. M. McClelland, “ML-OS-SIM,” GitHub, https://github.com/edward-n-ward/ML-OS-SIM (2023).
15. R. Cao, Y. Chen, W. Liu, et al., “Inverse matrix based phase estimation algorithm for structured illumination microscopy,” Biomed. Opt. Express 9(10), 5037 (2018). [CrossRef]
16. D. Lim, K. K. Chu, and J. Mertz, “Wide-field fluorescence sectioning with hybrid speckle and uniform-illumination microscopy,” Opt. Lett. 33(16), 1819 (2008). [CrossRef]
17. D. Lim, T. N. Ford, K. K. Chu, et al., “Optically sectioned in vivo imaging with speckle illumination HiLo microscopy,” J. Biomed. Opt. 16(1), 1 (2011). [CrossRef]
18. Z. Liu, Y. Lin, Y. Cao, et al., “Swin Transformer: Hierarchical Vision Transformer using Shifted Windows,” arXiv, arXiv.2103.14030 (2021). [CrossRef]
19. K. He, X. Zhang, S. Ren, et al., “Deep residual learning for image recognition,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 2016-December (IEEE Computer Society, 2016), pp. 770–778.
20. X. Chen, S. Zhong, Y. Hou, et al., “Superresolution structured illumination microscopy reconstruction algorithms: a review,” Light: Sci. Appl. 12(1), 172 (2023). [CrossRef]
21. X. Zhang, Y. Chen, K. Ning, et al., “Deep learning optical-sectioning method,” Opt. Express 26(23), 30762 (2018). [CrossRef]
22. C. Chai, C. Chen, X. Liu, et al., “Deep learning based one-shot optically-sectioned structured illumination microscopy for surface measurement,” Opt. Express 29(3), 4010 (2021). [CrossRef]
23. Y. Zhang, K. Li, K. Li, et al., “Image Super-Resolution Using Very Deep Residual Channel Attention Networks,” arXiv, arXiv.1807.02758 (2018). [CrossRef]
24. J. Liang, J. Cao, G. Sun, et al., “SwinIR: Image Restoration Using Swin Transformer,” arXiv, arXiv.2108.10257 (2021). [CrossRef]
25. A. Dosovitskiy, L. Beyer, A. Kolesnikov, et al., “An Image is Worth 16×16 Words: Transformers for Image Recognition at Scale,” arXiv, arXiv.2010.11929 (2020). [CrossRef]
26. C. N. Christensen, M. Lu, E. N. Ward, et al., “Spatio-temporal Vision Transformer for Super-resolution Microscopy,” arXiv, arXiv.2203.00030 (2022). [CrossRef]
27. Z. Liu, J. Ning, Y. Cao, et al., “Video Swin Transformer,” arXiv, arXiv.2106.13230 (2021). [CrossRef]
28. E. Agustsson and R. Timofte, “NTIRE 2017 Challenge on Single Image Super-Resolution: Dataset and Study,” in IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, vol. 2017-July (IEEE Computer Society, 2017), pp. 1122–1131.
29. R. Rubio-Sánchez, S. E. Barker, M. Walczak, et al., “A Modular, Dynamic, DNA-Based Platform for Regulating Cargo Distribution and Transport between Lipid Domains,” Nano Lett. 21(7), 2800–2808 (2021). [CrossRef]
30. M. Langecker, V. Arnaut, J. List, et al., “DNA Nanostructures Interacting with Lipid Bilayer Membranes,” Acc. Chem. Res. 47(6), 1807–1815 (2014). [CrossRef]
31. R. Rubio-Sánchez, G. Fabrini, P. Cicuta, et al., “Amphiphilic DNA nanostructures for bottom-up synthetic biology,” Chem. Commun. 57(95), 12725–12740 (2021). [CrossRef]
32. D. Y. Zhang and E. Winfree, “Control of DNA Strand Displacement Kinetics Using Toehold Exchange,” J. Am. Chem. Soc. 131(47), 17303–17314 (2009). [CrossRef]
33. D. Y. Zhang and G. Seelig, “Dynamic DNA nanotechnology using strand-displacement reactions,” Nat. Chem. 3(2), 103–113 (2011). [CrossRef]