Untrained neural network enhances the resolution of structured illumination microscopy under strong background and noise levels

Structured illumination microscopy (SIM) has been widely applied in the superresolution imaging of subcellular dynamics in live cells. Higher spatial resolution is expected for the observation of finer structures. However, further increasing spatial resolution in SIM under the condition of strong background and noise levels remains challenging. Here, we report a method to achieve deep resolution enhancement of SIM by combining an untrained neural network with an alternating direction method of multipliers (ADMM) framework, i.e., ADMM-DRE-SIM. By exploiting the implicit image priors in the neural network and the Hessian prior in the ADMM framework associated with the optical transfer model of SIM, ADMM-DRE-SIM can further realize the spatial frequency extension without the requirement of training datasets. Moreover, an image degradation model containing the convolution with equivalent point spread function of SIM and additional background map is utilized to suppress the strong background while keeping the structure fidelity. Experimental results by imaging tubulins and actins show that ADMM-DRE-SIM can obtain the resolution enhancement by a factor of ~1.6 compared to conventional SIM, evidencing the promising applications of ADMM-DRE-SIM in superresolution biomedical imaging.