Computational Super-Sectioning for Single-Slice Structured-Illumination Microscopy

While structured-illumination microscopy (SIM) is inherently a three-dimensional (3-D) technique, many biological questions can be addressed from the acquisition of a single focal plane with high lateral resolution. Unfortunately, the single-slice reconstruction of thick samples suffers from defocusing. In this paper, however, we take advantage of a 3-D model of the acquisition system to derive a reconstruction method out of a single two-dimensional (2-D) SIM measurement. It enables the estimation of the out-of-focus signal and improves the quality of the reconstruction, without the need of acquiring additional slices. The proposed algorithm relies on a specific formulation of the optimization problem together with the derivation of computationally efficient proximal operators. These developments allow us to deploy an efficient inner-loop-free alternating-direction method of multipliers (ADMM), with guaranteed convergence.