A Structured Illumination Microscopy Framework with Spatial-Domain Noise Propagation.

Biological images captured by a microscope are characterized by heterogeneous signal-to-noise ratios (SNRs) across the field of view due to spatially varying photon emission and camera noise. State-of-the-art unsupervised structured illumination microscopy (SIM) reconstruction algorithms, commonly implemented in the Fourier domain, do not accurately model this noise and suffer from high-frequency artifacts, user-dependent choices of smoothness constraints making assumptions on biological features, and unphysical negative values in the recovered fluorescence intensity map. On the other hand, supervised methods rely on large datasets for training, and often require retraining for new sample structures. Consequently, achieving high contrast near the maximum theoretical resolution in an unsupervised, physically principled manner remains a challenging task. Here, we propose Bayesian-SIM (B-SIM), an unsupervised Bayesian framework to quantitatively reconstruct SIM data, rectifying these shortcomings by accurately incorporating all noise sources in the spatial domain. To accelerate the reconstruction process for computational feasibility, we devise a parallelized Monte Carlo sampling strategy for inference. We benchmark our framework on both simulated and experimental images, and demonstrate improved contrast permitting feature recovery at up to 25% shorter length scales over state-of-the-art methods at both high- and low-SNR. B-SIM enables unsupervised, quantitative, physically accurate reconstruction without the need for labeled training data, democratizing high-quality SIM reconstruction and expands the capabilities of live-cell SIM to lower SNR, potentially revealing biological features in previously inaccessible regimes.