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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Recycling MMGKS for Large Scale Dynamic and Stream
ing Data - Misha Kilmer (Tufts University)
DTSTART;TZID=Europe/London:20230327T114000
DTEND;TZID=Europe/London:20230327T123000
UID:TALK198199AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/198199
DESCRIPTION:In regularization\, edge-preserving constraints ha
ve received considerable attention due to the need
for reconstructing high-quality images with sharp
edges. The use of the $\\ell_q$-norm in the gradi
ent of the image in the regularization term has sh
own potential for preserving edges in reconstructi
ons. One typically replaces the $\\ell_q$-norm ter
m with a sequence of $\\ell_2$-norm weighted gradi
ent terms with the weights determined from the cur
rent solution estimate. To overcome the large dime
nsionality\, (hybrid) Krylov subspace methods can
be employed to solve the 2-norm regularized proble
ms. One disadvantage\, however\, is the need to ge
nerate a new Krylov subspace from scratch for ever
y new two-norm regularized problem.\nThe majorizat
ion-minimization Krylov subspace method (MMGKS) co
mbines norm reweighting with generalized Krylov su
bspaces (GKS) to solve the reweighted problem. Aft
er projecting the problem using a small dimensiona
l subspace that expands each iteration\, the regul
arization parameter is selected. Basis expansion r
epeats until a sufficiently accurate solution is f
ound. Nevertheless\, for large-scale problems that
require many expansion steps to converge\, storag
e and the cost of repeated orthogonalizations may
present overwhelming memory and computational requ
irements.\nIn this talk we discuss a new method\,
RMMGKS\, that keeps the memory requirements bounde
d through recycling the solution subspace by alter
nating between enlarging and compressing the GKS s
ubspace. Numerical examples from dynamic photoacou
stic tomography and streaming X-ray CT imaging are
used to illustrate the effectiveness of the descr
ibed methods. \; \;This is joint work wit
h Mirjeta Pasha and Eric de Sturler.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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