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CATEGORIES:Statistics
SUMMARY:Analysis of regularized inversion of data corrupte
d by white Gaussian noise - Hanne Kekonnen
DTSTART;TZID=Europe/London:20171020T160000
DTEND;TZID=Europe/London:20171020T170000
UID:TALK89651AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/89651
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 physical quantity u\nM = Au + d*N\nwhere A is
linear smoothing operator and d > 0 is noise magn
itude.\n\nIf N was an L2-function we could use the
classical Tikhonov regularization to achieve an e
stimate. However\, realizations of white Gaussian
noise are almost never in L2. That is why we prese
nt a modification of Tikhonov regularization theor
y covering the case of white Gaussian measurement
noise. We will also consider the question in which
space does the estimate convergence to a correct
solution when the noise amplitude tends to zero an
d what is the speed of the convergence.\nThis is j
oint work with Matti Lassas and Samuli Siltanen (U
niversity of Helsinki).
LOCATION:MR12
CONTACT:Quentin Berthet
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