Mathematical microscopy

Summary form only given. Important improvements and breakthroughs in microscopy acquisition methods can be achieved by incorporating innovative signal/image processing ingredients directly into the acquisition and/or reconstruction protocols, and by developing the new paradigm of mathematical microscopy. First, we will present some recent developments of smart acquisition methods in digital holography imaging whereby it is possible with compressed sensing-based computational tools to recover a high quality image from very fewer samples than the full acquisition and to design smart dynamic imaging protocols. Then, we will present a new framework for Structured Illumination Microscopy (SIM) which is based on a Bayesian inverse problem formulation approach that enables the computation of one high-resolution image from a reduced number of low-resolution images and has no specific constraints on the modulation pattern. We will demonstrate the efficiency of this approach through numerical evaluations on simulated data and examples on real microscopy data.