Super-resolution structured illumination microscopy (SIM) has become a widely used method for biological imaging. Standard reconstruction algorithms, however, are prone to generate noise-specific artifacts that limit their applicability for lower signal-to-noise data. Here we present a physically realistic noise model that explains the structured noise artifact, which we then use to motivate new complementary reconstruction approaches. True-Wiener-filtered SIM optimizes contrast given the available signal-to-noise ratio, and flat-noise SIM fully overcomes the structured noise artifact while maintaining resolving power. Both methods eliminate ad hoc user-adjustable reconstruction parameters in favor of physical parameters, enhancing objectivity. The new reconstructions point to a trade-off between contrast and a natural noise appearance. This trade-off can be partly overcome by further notch filtering but at the expense of a decrease in signal-to-noise ratio. The benefits of the proposed approaches are demonstrated on focal adhesion and tubulin samples in two and three dimensions, and on nanofabricated fluorescent test patterns.

We compare two recently developed multiple-frame deconvolution approaches for the reconstruction of structured illumination microscopy (SIM) data: the pattern-illuminated Fourier ptychography algorithm (piFP) and the joint Richardson-Lucy deconvolution (jRL). The quality of the images reconstructed by these methods is compared in terms of the achieved resolution improvement, noise enhancement, and inherent artifacts. Furthermore, we study the issue of object-dependent resolution improvement by considering the modulation transfer functions derived from different types of objects. The performance of the considered methods is tested in experiments and benchmarked with a commercial SIM microscope. We find that the piFP method resolves periodic and isolated structures equally well, whereas the jRL method provides significantly higher resolution for isolated objects compared to periodic ones. Images reconstructed by the piFP and jRL algorithms are comparable to the images reconstructed using the generalized Wiener filter applied in most commercial SIM microscopes. An advantage of the discussed algorithms is that they allow the reconstruction of SIM images acquired under different types of illumination, such as multi-spot or random illumination.