Abstract

Biological assays in which particles generated by cells bind to a surface and can be imaged to reveal the cells' location are ubiquitous in biochemical, pharmacological and medical research. In this talk, I will describe the physics of these processes, a 3D radiation-diffusion-adsorption-desorption partial differential equation, and present our novel parametrization of its solution (i.e., the observation model) in terms of convolutional operators. Then, I will present our proposal to invert this observation model through a functional optimization problem with group-sparsity regularization and explain the reasoning behind this choice of regularizer. I will also present the results needed to derive the accelerated proximal gradient algorithm for this problem, and justify why we chose to formulate the algorithm in the original function spaces where our observation model operates. Finally, I will briefly comment on our choice of discretization, and show the final performance of our algorithm in both synthetic and real data. arXiv preprints: arXiv:1710.0164 , arXiv:1710.01622