Toward Overcoming the Local Minimum Trap in MFBD
Final performance rept. 15 Mar 2012-14 Mar 2015
EMORY UNIV ATLANTA GA
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Multi-frame blind deconvolution MFBD requires solving an optimization problem with an objective function that may have many local minima. Standard numerical optimization methods may become trapped in one of these local minimum points, resulting in poor image reconstructions. The aim of this proposed research is to develop new computational approaches that help to overcome the local minimum trap for iterative MFBD algorithms. Success in this research requires new approaches in several, interrelated areas, including obtaining a good initial guess, improved regularization methods and approaches for choosing regularization parameters, mathematical analyses and efficient computational methods to reduce the parameter space, and development of efficient implicit filtering algorithms for large scale optimization problems. In the three years of this grant, we have developed software, investigated the use of implicit filtering methods to avoid local minima, considered Gaussian Markov random fields to improve regularization, and we have developed methods for sparsity constraints that can be used for large scale MFBD problems. The work done on this, and a previous AFOSR grant, initiated a very productive collaboration with Dr. Stuart Jefferies, IFA, University of Hawaii, Dr. Douglas Hope, U.S. Air Force Academy, and Dr. Michael Hart, Physics and Astronomy, University of Arizona.
- Numerical Mathematics
- Operations Research
- Computer Programming and Software