A primal-dual mathematical framework for particle reconstruction in electron microscopy

Abstract: In this talk, I would like to discuss a computational method as well as our proposed mathematical model for covariance matrix reconstruction. As a motivation for this work, I will begin with a brief history of the CryoEM single particle reconstruction in structural biology and present computational difficulties in particle reconstruction. Converting particle reconstruction to matrix reconstruction, I will propose a convex, yet non-differentiable, mathematical model. It turns out that its dual counterpart is written as semi-definite programming, which leads to a computationally efficient algorithm for the primal problem, based on optimality conditions. Basics of the primal-dual formulation in convex analysis will be provided for better understanding.