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CATEGORIES:CMIH seminar series
SUMMARY:Optimisation methods for Bayesian inference: Appli
cation to high dimensional inverse problems - Audr
ey Repetti\, Heriot-Watt University
DTSTART;TZID=Europe/London:20180601T140000
DTEND;TZID=Europe/London:20180601T150000
UID:TALK95446AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/95446
DESCRIPTION:An important number of scientific and technologica
l applications (ranging from healthcare to astrono
my) consist in solving high dimensional inverse pr
oblems\, where an unknown object is estimated from
the provided measurements. A common method to so
lve these problems is to rely on a Bayesian maximu
m a posteriori (MAP) approach. A main limitation o
f this approach is that it does not provide any in
formation regarding the uncertainty in the solutio
n delivered. This analysis is particularly importa
nt in imaging problems that are ill-posed or ill-c
onditioned\, for subsequent decision making proces
ses (e.g. decision concerning a tumor appearing on
a brain image from MRI). \nIn this presentation I
will present a methodology to probe the data and
perform uncertainty quantification. In the propose
d method\, we quantify the uncertainty associated
with particular structures appearing in the MAP es
timate\, obtained from a log-concave Bayesian mode
l. A hypothesis test is defined\, where the null
hypothesis represents the non-existence of the str
ucture of interest in the true image. To determine
if this null hypothesis is rejected\, we use the
data and prior knowledge. Computing such test in t
he context of imaging problem is often intractable
for state-of-the-art Markov chain Monte Carlo alg
orithms\, due to the high dimensionality involved.
In this work\, we formulate the Bayesian hypothes
is test as a convex minimization problem\, which i
s subsequently solved using a proximal primal-dual
algorithm. The proposed method is applied to astr
onomical and medical imaging.\n\nJoint work with M
arcelo Pereyra and Yves Wiaux
LOCATION:MR11\, Centre for Mathematical Sciences
CONTACT:Rachel Furner
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