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Recycling MMGKS for Large Scale Dynamic and Streaming Data

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RNTW02 - Rich and non-linear tomography in medical imaging, materials and non destructive testing

In regularization, edge-preserving constraints have received considerable attention due to the need for reconstructing high-quality images with sharp edges. The use of the $\ell_q$-norm in the gradient of the image in the regularization term has shown potential for preserving edges in reconstructions. One typically replaces the $\ell_q$-norm term with a sequence of $\ell_2$-norm weighted gradient terms with the weights determined from the current solution estimate. To overcome the large dimensionality, (hybrid) Krylov subspace methods can be employed to solve the 2-norm regularized problems. One disadvantage, however, is the need to generate a new Krylov subspace from scratch for every new two-norm regularized problem. The majorization-minimization Krylov subspace method (MMGKS) combines norm reweighting with generalized Krylov subspaces (GKS) to solve the reweighted problem. After projecting the problem using a small dimensional subspace that expands each iteration, the regularization parameter is selected. Basis expansion repeats until a sufficiently accurate solution is found. Nevertheless, for large-scale problems that require many expansion steps to converge, storage and the cost of repeated orthogonalizations may present overwhelming memory and computational requirements. In this talk we discuss a new method, RMMGKS , that keeps the memory requirements bounded through recycling the solution subspace by alternating between enlarging and compressing the GKS subspace. Numerical examples from dynamic photoacoustic tomography and streaming X-ray CT imaging are used to illustrate the effectiveness of the described methods.   This is joint work with Mirjeta Pasha and Eric de Sturler.

This talk is part of the Isaac Newton Institute Seminar Series series.

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