Title: A convex formulation for binary tomography
Speaker: Ajinkya Kadu, Mathematical Institute, Utrecht University (UU), The Netherlands
Time: 230pm, 7th March, 2019, Thursday
Venue: IEOR Seminar Room
Abstract: Binary tomography is concerned with the recovery of binary images from a few of their projections (i.e., sums of the pixel values along various directions). To reconstruct an image from noisy projection data, one can pose it as a constrained least-squares problem. As the constraints are non-convex, many approaches for solving it rely on either relaxing the constraints or heuristics. We propose a novel convex formulation, based on the Lagrange dual of the constrained least-squares problem. The resulting problem is an L_1 regularized least-squares problem which can be solved efficiently. It is a relaxation in the sense that it can only be guaranteed to give a feasible solution; not necessarily the optimal one. Through exhaustive experiments on small images we conjecture that if the problem has a unique solution, our dual approach finds it. In the case of multiple solutions, our approach finds the commonalities between the solutions. This is joint work with Dr. Tristan van Leeuwen (Utrecht University).
Short Bio: Ajinkya Kadu is a Ph.D. candidate at the Mathematical Institute of Utrecht University (UU) in The Netherlands. He works on 'geometric inverse problems' with Dr. Tristan van Leeuwen (UU), Prof. Wim Mulder (Shell/TU Delft) and Prof. Joost Batenburg (CWI Amsterdam). His application interests are computational tomography, acoustic and electromagnetic imaging. His Ph.D. project is part of Computational Sciences for Energy Research, a joint program of Netherland's science foundation and Shell Global Research. During his Ph.D., he spent time at the University of British Columbia in Vancouver, Mitsubishi Electric Research Labs in Cambridge, MA, and GeorgiaTech in Atlanta, GA. He graduated with B.Tech and M.Tech from Department of Aerospace Engineering at Indian Institute of Technology Bombay with a MTech Thesis on Operations Management (contracts design).