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SUMMARY:Analysis of regularized inversion of data corrupted by white Gauss
 ian noise - Hanne Kekonnen
DTSTART:20171020T150000Z
DTEND:20171020T160000Z
UID:TALK89651@talks.cam.ac.uk
CONTACT:Quentin Berthet
DESCRIPTION:Our aim is to provide new analytic insight to the relationship
  between the continuous and practical inversion models corrupted by white 
 Gaussian noise. Let us consider an indirect noisy measurement M of a physi
 cal quantity u\nM = Au + d*N\nwhere A is linear smoothing operator and d >
  0 is noise magnitude.\n\nIf N was an L2-function we could use the classic
 al Tikhonov regularization to achieve an estimate. However\, realizations 
 of white Gaussian noise are almost never in L2. That is why we present a m
 odification of Tikhonov regularization theory covering the case of white G
 aussian measurement noise. We will also consider the question in which spa
 ce does the estimate convergence to a correct solution when the noise ampl
 itude tends to zero and what is the speed of the convergence.\nThis is joi
 nt work with Matti Lassas and Samuli Siltanen (University of Helsinki).
LOCATION:MR12
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