Sparse reconstruction from Multiple-Angle Total Internal Reflection fluorescence Microscopy

Super-resolution microscopy techniques allow to overstep the diffraction limit of conventional optics. Theses techniques are very promising since they give access to the visualisation of finer structures which is of fundamental importance in biology. In this paper we deal with Multiple-Angle Total Internal Reflection Microscopy (MA-TIRFM) which allows to reconstruct 3D sub-cellular structures of a single layer of ~ 300 nm behind the glass coverslip with a high axial resolution. The 3D volume reconstruction from a set of 2D measurements is an ill-posed inverse problem and a regularization is essential. Our aim in this work is to propose a new reconstruction method for sparse structures robust to Poisson noise and background fluorescence. The sparse property of the solution can be seen as a regularization using the `£° norm´. In order to solve this combinatorial problem, we propose a new algorithm based on smoothed `£° norm´ allowing minimizing a non convex energy, composed of the Kullback-Leibler divergence data term and the £° regularization term, in a Graduated Non Convexity framework.