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SUMMARY:Recycling MMGKS for Large Scale Dynamic and Streaming Data - Misha
  Kilmer (Tufts University)
DTSTART:20230327T104000Z
DTEND:20230327T113000Z
UID:TALK198199@talks.cam.ac.uk
DESCRIPTION:In regularization\, edge-preserving constraints have received 
 considerable attention due to the need for reconstructing high-quality ima
 ges 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 deter
 mined from the current solution estimate. To overcome the large dimensiona
 lity\, (hybrid) Krylov subspace methods can be employed to solve the 2-nor
 m regularized problems. One disadvantage\, however\, is the need to genera
 te a new Krylov subspace from scratch for every new two-norm regularized p
 roblem.\nThe majorization-minimization Krylov subspace method (MMGKS) comb
 ines norm reweighting with generalized Krylov subspaces (GKS) to solve the
  reweighted problem. After projecting the problem using a small dimensiona
 l subspace that expands each iteration\, the regularization parameter is s
 elected. Basis expansion repeats until a sufficiently accurate solution is
  found. Nevertheless\, for large-scale problems that require many expansio
 n steps to converge\, storage and the cost of repeated orthogonalizations 
 may present overwhelming memory and computational requirements.\nIn this t
 alk we discuss a new method\, RMMGKS\, that keeps the memory requirements 
 bounded through recycling the solution subspace by alternating between enl
 arging and compressing the GKS subspace. Numerical examples from dynamic p
 hotoacoustic tomography and streaming X-ray CT imaging are used to illustr
 ate the effectiveness of the described methods.&nbsp\; &nbsp\;This is join
 t work with Mirjeta Pasha and Eric de Sturler.
LOCATION:Seminar Room 1\, Newton Institute
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