Session S08 - Inverse Problems and Applications

Friday, July 23, 16:30 ~ 17:00 UTC-3

Efficient Edge-Preserving Methods for Large-Scale Dynamic Inverse Problems.

Mirjeta Pasha

Arizona State University, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In this talk we consider numerical methods for computing the maximum a posteriori (MAP) estimator for time dependent inverse problems, where the target of interest changes during the measurement process as well as the operator that models the forward problem. For example, solving the limited angle tomography problem is challenging because of both its dynamic nature and the limited amount of data available. Moreover, incorporating spatial and temporal information about the prior and providing properties like edge-preserving can be computationally not attractive. Hence, we propose efficient and effective edge-preserving and sparsity promoting iterative regularization methods that incorporate spatial and temporal information by introducing regularizers that enforce simultaneous regularization in space and time, and that typically enhance edges (at each time instant) and enforce proximity (at consecutive time instants) by total variation (TV) and group sparsity. The methods that we develop here are iterative methods based on majorization minimization strategy with quadratic tangent majorant that allow the resulting least squares problem to be solved with a generalized Krylov subspace method for large scale problems. The regularization parameter can be defined automatically and at a low cost in the projected subspaces of a relatively small dimension. Numerical examples from a wide range of applications like limited angle computerized tomography (CT), space-time deblurring, and photoacoustic tomography (PAT) illustrate the effectiveness of the described approaches.

Joint work with Malena Espanol (Arizona State University, USA), Silvia Gazzola (Universoty of Bath, UK), Arvind Saibaba (North Carolina State University, USA ) and Eric de Sturler (Virginia Tech, USA).

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