MSTuD15
Inverse problems in PDE and probability  Part I of II
For Part II, see MSTuE15
Date: August 11
Time: 13:3015:30
Room: 213B
(Note: Click title to show the abstract.)
Organizer:
Helin, Tapio (Univ. of Helsinki)
Hyvonen, Nuutti (Aalto Univ.)
Abstract: The aim of the minisymposium is to highlight new research results in inverse problems that involve stochastic modelling and partial differential equations. All aspects of such inversion are discussed, including mathematical analysis, computational techniques, and experimental results.
MSTuD151
13:3014:00
A Bayesian level set method for geometric inverse problems
Lu, Yulong (Univ. of Warwick)
Abstract: We develop a novel Bayesian level set approach for geometric inverse problems that arise in PDEconstrained applications. Our work consists of a rigorous application of the infinitedimensional Bayesian framework whereby proving the measurability of the observational map that arises from our levelset representation enables us to show existence and wellposedness of the posterior measure. The method is applied to solve two model problems: inverse source problem and groundwater flow problem.
MSTuD152
14:0014:30
Spectral approximations for iterative inversion methods: A parabolic case
Mustonen, Lauri (Aalto Univ.)
Abstract: In the context of nonlinear inverse problems, we present an efficient way to construct the linear subproblems of a GaussNewtonian iteration. The method is based on solving the forward problem in a highdimensional parameter domain by using spectral methods, resulting in a numerical solution that depends explicitly on the parameters. As an example we study the inverse boundary value problem of a parabolic partial differential equation.
MSTuD153
14:3015:00
Detecting stochastic inclusions in electrical impedance tomography
Harrach, Bastian (Univ. of Stuttgart,)
Abstract: (This is a joint work with A. Barth, N. Hyvönen and L. Mustonen.)
We consider the inclusion detection problem of electrical impedance tomography with stochastic conductivities. We show that a conductivity anomaly with a random conductivity can be identified by applying the Factorization Method or the Monotonicity Method to the mean value of the corresponding NeumanntoDirichlet map provided that the anomaly has high enough contrast.
MSTuD154
15:0015:30
Edgepromoting reconstruction of absorption and diffusivity in optical tomography
Majander, Helle (Aalto Univ.)
Abstract: Diffuse optical tomography is an imaging modality for determining the diffusion and absorption distributions inside a highly scattering object. This is done by guiding nearinfrared light to the surface of the object and observing the light propagation by the detectors on the surface. In this talk we assume that both properties contain distinct inclusions in a constant background. We introduce an iterative algorithm for simultaneously reconstructing the diffusion and absorption using edgepreferring priors.
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Footnote: Code: TypeDateTimeRoom No.
Type : IL=Invited Lecture, SL=Special Lectures, MS=Minisymposia, IM=Industrial Minisymposia, CP=Contributed Papers, PP=Posters
Date: Mo=Monday, Tu=Tuesday, We=Wednesday, Th=Thursday, Fr=Friday
Time : A=8:309:30, B=10:0011:00, C=11:1012:10, BC=10:0012:10, D=13:3015:30, E=16:0018:00, F=19:0020:00, G=12:1013:30, H=15:3016:00
Room No.: TBA
