A physically accurate framework for structured illumination microscopy in the spatial domain

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 noisy detector electronics. This noise overwhelms high frequency signal or short length scale features already weakened by diffraction, leading to resolution loss. State of the art unsupervised structured illumination microscopy (SIM) algorithms that recover high frequency features beyond diffraction limit, however, do not accurately model this noise and are unable to achieve the maximum possible resolution. Furthermore, SIM reconstructions often suffer from unphysical smoothing and may return negative values. Here, we demonstrate a parallelizable and unsupervised framework to quantitatively reconstruct fluorescence profiles from SIM images. We naturally work in the spatial domain within the Bayesian paradigm to incorporate all noise sources in a physically accurate manner, and estimate strictly positive fluorescence profiles using Monte Carlo methods. We apply our framework on both simulated and experimental images, and demonstrate resolution improvement of up to 20% over state-of-the-art methods even at high SNR. Additionally, we are able to recover fluorescence profiles at resolution beyond the diffraction limit even when average photon counts are low (<40 per exposure), potentially allowing for imaging with reduced phototoxicity.