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Speaker: Maryam Yashtini,  Georgia Institute of Technology

Title: Fast Alternating Minimization Algorithms for Inverse Problems in Imaging

Abstract: This talk focuses on the development of fast numerical methods for solving a few inverse problems arising in medical imaging and image processing applications. The common theme of these problems is that the minimizing functional involves non-differentiable terms. In addition, the first inverse problem is highly ill-conditioned; hence the solution of linear system is prone to have extreme numerical errors. The second problem also involves a non-convex curvature term and is highly nonlinear so that the traditional sub-gradient methods converge very slowly. To tackle the computational complexities, I use relaxation and approximation techniques. In addition, I exploit splitting variables and alternating direction method of multipliers to decouple the original challenging problems into sub-problems which are easier to solve. To obtain fast results, I develop innovative line search strategies and solve the sub-problems using Fourier transforms and shrinkage operators. I present the analytical properties of these methods as well as various numerical experiments on parallel Magnetic Resonance Imaging and image inpainting problems. The comparison with other methods are given to show the efficiency and the effectiveness of the proposed methods.

Refreshments are available at 3:00 PM in SC 313F.

The department colloquia are held every Thursday (excluding holidays) at 3:35 pm in room SC 323 unless otherwise noted. All are invited to attend.