Estimation-free spatial-domain image reconstruction of structured illumination microscopy

Structured illumination microscopy (SIM) achieves super-resolution (SR) by modulating the high-frequency information of the sample into the passband of the optical system and subsequent image reconstruction. The traditional Wiener-filtering-based reconstruction algorithm operates in the Fourier domain, it requires prior knowledge of the sinusoidal illumination patterns which makes the time-consuming procedure of parameter estimation to raw datasets necessary, besides, the parameter estimation is sensitive to noise or aberration-induced pattern distortion which leads to reconstruction artifacts. Here, we propose a spatial-domain image reconstruction method that does not require parameter estimation but calculates patterns from raw datasets, and a reconstructed image can be obtained just by calculating the spatial covariance of differential calculated patterns and differential filtered datasets (the notch filtering operation is performed to the raw datasets for attenuating and compensating the optical transfer function (OTF)). Experiments on reconstructing raw datasets including nonbiological, biological, and simulated samples demonstrate that our method has SR capability, high reconstruction speed, and high robustness to aberration and noise.