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Cell Detection by Functional Inverse Diffusion and Group Sparsity

Presented by: 
Pol del Aguila Pla KTH - Royal Institute of Technology
Thursday 2nd November 2017 - 15:40 to 16:00
INI Seminar Room 1
Biological assays in which particles generated by cells bind to a surface and can be imaged to reveal the cells' location and secretion properties are ubiquitous in biochemical, pharmacological and medical research. In this talk, I will first describe the physics of the problem, a 3D radiation-diffusion-adsorption-desorption PDE system, and present our novel parametrization of its solution in terms of convolutional operators. Secondly, I will present the functional optimization problem with group-sparsity regularization we propose to invert the problem and explain the physical, mathematical and heuristic reasoning behind our choice of regularizer. Thirdly, I will present the proofs needed to apply the accelerated proximal gradient algorithm to our problem, and justify why we chose to formulate the algorithm in the original function spaces that characterize the physical problem. Finally, I will present the details of the discretization we used to implement the resulting algorithm, and show its final performance both in simulated and real data.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons