Quantitative image reconstruction for microscopy with correct sub-pixel photon statistics

The diffraction of light forces a lower limit on spatial resolution available with conventional optical microscopes. However, sophisticated computational techniques in conjunction with inhomogeneous illumination have facilitated image acquisition without this limitation. Typical image reconstruction algorithms for such superresolution microscopy techniques, including structured illumination microscopy (SIM), involve combining multiple diffraction-limited raw images in Fourier space via minimization of some cost function. This leads to undesired artifacts including loss of correct noise properties for the photons collected by the camera and loss of temporal resolution. Here, we propose a Bayesian framework performing reconstructions in real space while incorporating all sources of noise such as camera electronics and incoming photon Poisson statistics. Furthermore, this framework inherently allows corrections for inhomogeneous illumination incident on a biological sample. As a result, superresolution reconstructions can now be performed with fewer images otherwise needed by existing reconstruction methods while maintaining Poisson statistics for collected photons at the sub-pixel level. We benchmark our framework using both simulated and experimentally generated images.