Speckle blind SIM with calibration targets

In fluorescence microscopy, the unknown sample ρ is related to a series of low-resolution acquisitions {ym}m=1 via the convolution model ym = h ⊗ (ρ × Im) + m, with h the microscope point spread function that exhibits a bounded Fourier support DPSF, Im the m-th illumination pattern and m an additive noise component. When Im is homogeneous, the sample frequencies inside DPSF are the only ones that can be retrieved from the dataset, hence limiting the image resolution. Following [1], a super-resolved estimate of ρ can nevertheless be achieved with speckle illuminations. Thanks to a mathematical refoundation of this technique [2], the super-resolution mechanism of this technique is now understood and a very fast numerical implementation has been derived and recently tested with real data. More specifically, some ArgoLight test patterns imaged with a home-made fastSIM setup [3] leads to a super-resolution factor higher than 1.8 after reconstruction.