Nonsmooth Convex Optimization for Structured Illumination Microscopy Image Reconstruction

In this paper, we propose a new approach for structured illumination microscopy image reconstruction. We first introduce the principles of this imaging modality and review its properties in various conditions. We then propose the minimization of nonsmooth convex functionals for the recovery of the unknown image and investigate several data–fitting and regularization terms in order to tackle reconstruction of noisy data. More specifically, we consider an original approach based on sparse local patch dictionaries for the regularization of the estimate. We demonstrate the good performance of the proposed approach on a test benchmark and perform some test experiments on images acquired on two different microscopes.