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SUMMARY:Learned forward operators: Variational regularization for black-bo
 x models - Jonas Adler (KTH - Royal Institute of Technology )
DTSTART:20171031T154000Z
DTEND:20171031T160000Z
UID:TALK94123@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:In inverse problems\, correct modelling of the forward model i
 s typically one of the most important components to obtain good reconstruc
 tion quality. Still\, most work is done on highly simplified forward model
 s. For example\, in Computed Tomography (CT)\, the true forward model\, gi
 ven by the solution operator for the radiative transport equation\, is typ
 ically approximated by the ray-transform. The primary reason for this gros
 s simplification is that the higher quality forward models are both comput
 ationally costly\, and typically do not have an adjoint of the derivative 
 of the forward operator that can be feasibly evaluated.   The community is
  not un-aware of this miss-match\, but the work has been focused on &ldquo
 \;the model is right\, lets fix the data&rdquo\;. We instead propose going
  the other way around by using machine learning in order to learn a mappin
 g from the simplified model to the complicated model using deep neural net
 works. Hence instead of learning how to correct complicated data so that i
 t matches a simplified forward model\, we accept that the data is always r
 ight and instead correct the forward model.   We then use this learned for
 ward operator\, which is given as a composition of a simplified forward op
 erator and a convolutional neural network\, as a forward operator in a cla
 ssical variational regularization scheme. We give a theoretical argument a
 s to why correcting the forward model is more stable than correcting the d
 ata and provide numerical examples in Cone Beam CT reconstruction.
LOCATION:Seminar Room 1\, Newton Institute
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