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In this talk, we explore some practical strategies of incorporating outside information into a Krylov subspace method for image reconstruction, focusing mainly on augmented Krylov subspace methods. Many variants of these methods have been been proposed by different authors for the improvement of the reconstruction and acceleration of the semiconvergence, particularly in the case where one augments with known sharp edge features and jumps. However, what can one do in a more practical setting, where one may not know where any of these features are? We discuss here some new methods and ideas moving towards answering this question.
This presentation is part of Minisymposium “MS8 - Krylov Methods in Imaging: Inverse Problems, Data Assimilation, and Uncertainty Quantification (2 parts)”
organized by: Arvind Saibaba (North Carolina State University) , Julianne Chung (Virginia Tech) , Eric de Sturler (Virginia Tech) .