Structured illumination microscopy (SIM), as one of the most promising super-resolution techniques for bioscience, offers unprece­dented oppor­tunities for live-cell investigation due to its merits of full-field imaging, fast image acquisition, and high photon efficiency. Despite these advantages, SIM still suffers from several technical challenges since high-quality SIM reconstructions rely heavily on post-processing algorithms, particularly precise knowledge about the illumina­tion parameters, minor errors of which may even have a significant impact on the reconstruc­tion results, resulting in substantial reconstruction artifacts. Moreover, these parameters are sample- and environ­ment-dependent, so they cannot be compensated by one-time calibration, necessi­tating posterior restoration from the acquired experimental data unless the experi­mental environment is harshly maintained stable.

Although many algorithms have been proposed to estimate illumination parameter, the conflict between accuracy and speed and the vulnera­bility to low signal-to-noise ratios (SNRs) hinder the practical appli­cation and widespread adoption of SIM in the biomedical community for high-speed, real-time, long-term live-cell imaging, where low photobleaching, photo­toxicity, and light dose are a must, with the consequent more severe low SNR. Now, a team of scientists led by Qian Chen and Chao Zuo from Nanjing University of Science and Techno­logy have developed a new SIM algorithm. The efficient and robust algorithm could be a promising method for real-time, long-term, super-resolution imaging of live cells.

The researchers discovered that the ideal phasor matrix of a SIM pattern is of rank one, which means that it should have only one principal component, describing the single best subspace of the data in the least-squares sense. However, under real conditions, experi­mental imperfections (e.g., noise, optical aberrations, OTF-induced signal attenua­tion, dysregulated modulation depth) and other distur­bances will inevitably produce noisy measurements, resulting in high dimen­sionality of the pattern phasor matrix. Therefore, eliminating these irrelevant disturbances and finding the first principal component of the high-dimensional pattern phasor matrix is the key to the success of robust parameter estimation for SIM under low SNR conditions.

Principal component analysis (PCA) is a non-iterative dimensionality reduction tool by geometrically projecting data onto lower subspace called principal components, with the goal of finding the best summary of the data using a limited number of principal components, which just coincides with the task of accurately estimating the illumination parameters from the phasor matrix. By intro­ducing PCA, the unwanted noise and other disturbances in the raw pattern phasor matrix are effectively cleaned up after dimen­sionality reduction to extract the desired, parameter-dominating principal component without reference to prior knowledge, thus precisely and efficiently identifying noninteger pixel wave vectors and pattern phases.

However, PCA itself can be a time-consuming operation for relatively large matrix dimensions. The researchers derived that the inverse Fourier spectrum of an ideal pattern phasor matrix is a down-sampled 2D Dirichlet function with most of its energy concen­trated in limited support. Therefore, a frequency domain mask is applied to significantly reduce the amount of data involved in the PCA computation while further rejecting the inter­ference of the noise components, confering PCA-SIM lower computa­tional complexity and better robustness to low SNRs.

Experiments demonstrate that PCA-SIM achieves more accurate parameter estimation and superior noise immunity with more efficient non-iterative efficiency than conventional iterative corre­lation-based approach. “High accuracy, efficiency and robust­ness advantages pio­neeringly enable flexible, real-time, high-quality SIM super-resolution imaging of live cells with on-the-fly adaptive illumi­nation parameter compensation based on PCA-SIM under complex experimental conditions,” Zuo an colleagues said. “PCA-SIM has the potential to facilitate new biological disco­veries and open up new possi­bilities for solving problems in cell biology, cancer research, develop­mental biology and neuroscience.” (Source: LPC CAS)

Reference: J. Qian et al.: Structured illumination microscopy based on principal component analysis, eLight 3, 4 (2023); DOI: 10.1186/s43593-022-00035-x

Link: Smart Computational Imaging (SCI) Laboratory, Nanjing University of Science and Technology, Nanjing, China