Parallel session 6
Thu, 13:30-15:30



M16-I: EFFICIENT RECONSTRUCTION METHODS FOR ELECTRICAL IMPEDANCE TOMOGRAPHY AND INVERSE SCATTERING (PART 1)

ORGANIZERS: Roland Griesmaier, Nuutti Hyvonen

TALKS & SPEAKERS:

Multi-frequency MUSIC for electrical impedance tomography
Roland Griesmaier

Sampling Methods and Interior Eigenvalues
Armin Lechleiter

Two-electrode-measurements in EIT
Stefanie Hollborn

A generalized linear sampling method for identifying cracks in unknown background
Lorenzo Audibert



M19: INVERSE TRANSPORT AND OPTICAL TOMOGRAPHY

ORGANIZERS: Manabu Machida (chair: Tanja Tarvainen)

TALKS & SPEAKERS:

Quantitative PhotoAcoustic Tomography using the Radiative Transfer Equation
Simon Arridge

Truncated Fourier-series approximation of the time-dependent radiative transfer equation
Tanja Tarvainen

Combinatorial Inverse Problems
Jeremy Hoskins

Optical tomography with three-dimensional singular eigenfunctions
Manabu Machida    ***CANCELLED***



M14-II: AGGREGATION AND JOINT INVERSION. CHALLENGES FOR NUMERICAL REGULARIZATION METHODS (PART 2)

ORGANIZERS: Sergei Pereverzyev, Volker Michel

TALKS & SPEAKERS:

Combining Downward Continuation and Local Approximation for Harmonic Potentials
Christian Gerhards

Multi-penalty regularization for detecting relevant variables
Sergiy Pereverzyev Jr

Two-parameter regularization of ill-posed spherical pseudo-differential equations in the C-space
Pavlo Tkachenko

The Regularized Orthogonal Functional Matching Pursuit for Ill-Posed Inverse Problems
Roger Telschow



M38-I: INVERSE BOUNDARY VALUE PROBLEMS FOR ELLIPTIC SYSTEMS (PART 1)

ORGANIZERS: Francis Chung, Mikko Salo

TALKS & SPEAKERS:

On the determination of finitely many parameters in some elliptic systems of elasticity from boundary measurements
Elena Beretta    ***CANCELLED***

On uniqueness of an inverse problem for the time harmonic Maxwell equations
Pedro Caro

An Hs,p(Ω;curl) estimate for the Maxwell system
Manas Kar

An inverse boundary problem for the Stokes equations in the plane
Ru-Yu Lai

An inverse problem for the Hodge Laplacian
Francis Chung



M5-I: AUTOCONVOLUTION AND RELATED NONLINEAR ILL-POSED PROBLEMS (PART 1)

ORGANIZERS: Bernd Hofmann, Jens Flemming

TALKS & SPEAKERS:

Deconvolution and decorrelation problems in the physics of femtosecond lasers
Gunter Steinmeyer

Revisiting the Lavrentiev method for nonlinear ill-posed problems
Elena Resmerita

An inverse problem for fractional diffusion equation with integral over-determination
Jaan Janno

On a nonstationary Iterative Method for solving Inverse Problems in Hilbert Spaces
Qinian Jin



M8-III: CURRENT DEVELOPMENTS IN TOMOGRAPHY: FROM ALGORITHMS TO APPLICATIONS (PART 3)

ORGANIZERS: Jurgen Frikel, Esther Klann, Todd Quinto

TALKS & SPEAKERS:

ART Performance
Per Christian Hansen

Broken ray tomography
Joonas Ilmavirta

Incorporating Material-Specific Priors in a CT Reconstruction-Segmentation Algorithm
Mikhail Romanov

Reconstruction in quantitative photoacoustic tomography by using sparse representations
Giovanni Alberti



M17: INVERSE SOURCE PROBLEMS IN ENGINEERING APPLICATIONS

ORGANIZERS: Balgaisha Mukanova, Alemdar Hasanoglu

TALKS & SPEAKERS:

Nonlinear inverse problem for a filtration model: numerical recovery of parameters
Balgaisha Mukanova

Inverse Source Problems for Euler-Bernoulli Beam Equation
Alemdar Hasanoglu

Identification of a convolution kernel in a nonlinear wave equation
Lukas Seliga

An inverse source problem in parabolic partial differential equations
Marian Slodicka



M40-III: OPTIMISING INVERSION MODELS (PART 3)

ORGANIZERS: Juan Carlos De Los Reyes, Eldad Haber, Carola Schonlieb

TALKS & SPEAKERS:

Pitfalls in Bayesian inversion
Martin Burger

Approximate marginalization of absorption and scattering in fluorescence diffuse optical tomography
Ville Kolehmainen

Large-scale Bayesian inference for nonlinear inverse problems
Noemi Petra

Wavefield-reconstruction inversion
Bas Peters



CT2: APPLIED ANALYSIS

ORGANIZERS: Michael Music

TALKS & SPEAKERS:

Uniqueness in the identification of damage in vibrating beams and plates
Alexandre Kawano

Multiple time-dependent coefficient identification thermal problems
Daniel Lesnic

Reconstruction of slowly-moving dipoles in an inverse source problem for a three dimensional scalar wave equation
Takashi Ohe

Solutions to the Novikov-Veselov equation via the inverse scattering method
Michael Music



Introducing special speakers

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  • Gitta Kutyniok from TU Berlin is an expert on "sparsity-promoting" reconstruction methods. Inverse problems are about recovering objects based on measurement data which is insufficient. The data needs to be complemented with extra information about the object, such as sparsity. Sparsity means representing the object using building blocks specifically chosen so that only very few of them are needed. Professor Kutyniok often uses "shearlets" for representing images. Shearlets are versatile building blocks adapting to image details of any scale and representing edges with a variety of orientations.

    In the attached picture she applies shear let reconstruction to an inverse scattering problem, resulting in a result much improved over a traditional method. In her plenary talk at the AIP2015 conference, Professor Kutyniok gives an introduction to the theory and computational use of the shearlet transform.

  • Peter Markowich from KAUST is an expert of partial differential equations which arise from systems depending on many variables and involving change. Due to the generality of mathematics, such models apply to wildly different areas of application.

    In his Special Keynote Address, Professor Markowich discusses biological transportation networks, price formation in economic markets and fluid flow in porous matter. The picture shows models for a large crowd of people in three groups exiting a building as fast as possible. Different models of human behaviour lead to different dynamics. This is a joint work with Martin Burger, Marco Di Francesco and Marie-Therese Wolfram.

  • Peijun Li from Purdue University studies direct and inverse scattering problems. One of the central contributions in his work is the design of imaging methods accepting realistic near-field measurements (as opposed to mathematically ideal far-field patterns). In the picture is shown reconstructions of a two-dimensional shape. Here the unknown shape is probed with acoustic waves send from different directions. Various datasets are considered with limited angles of view. Observe that the "dark side" of the shape is more difficult to recover. This work is joint between Peijun Li and Yuliang Wang.

    In his plenary talk at AIP, Peijun Li will describe his recent work on achieving sub-wavelength resolution for inverse surface scattering problems.

  • Hongyu Liu from Hong Kong Baptist University knows how to recover objects from remote measurements. Below is an example of sending elastic vibrations through an unknown body, and recovering inhomogeneities (red) inside. This 2013 result is a joint work between four authors: Guanghui Hu, Jingzhi Li, Hongyu Liu and Hongpeng Sun.

    At AIP, Professor Liu will explain how to hide objects from remote sensing. Such cloaking techniques are already used widely in fiction: think Harry Potter and his invisibility cloak.

  • Xiaoqun Zhang from Shanghai Jiao Tong University is an expert in inverse problems related to image processing. Here is an example of her work (this one done jointly with Tony Chan). On the left is the original "Barbara" image. Second image from left shows many missing pixels that should be filled back in using so-called "inpainting." Third image from left shows the result of a standard baseline technique, whereas the rightmost picture shows the excellent inpainting result using a nonlocal method developed by Zhang & Chan in 2010.

  • Recent work of Thomas Schuster from Saarland University, Germany, (joint with Arne Wöstehoff) paves the way to self-diagnosing airplanes. The idea is to equip the aircraft with vibration sources and sensors. Cracks and other defects can be detected by sending vibrations along the plane, and measuring the response at the sensors.

    Prof. Schuster's plenary talk at AIP will be about vector tomography, which allows new imaging techniques in the fields of medicine, industry, oceanography, plasma physics, polarization tomography and electron microscopy.

  • Katya Krupchyk from University of California at Irvine, USA. Professor Krupchyk is an expert on mathematical models of a range of indirect physical measurements. In one of her works, joint with Matti Lassas and Samuli Siltanen, she studied an extension of the imaging method called electrical impedance tomography.

    In this work, electrical voltage-to-current measurements are preformed on the boundary of a physical body. The resulting currents flowing inside the body produce heat. The surface of the body is covered with heat flow sensors (interlaced with electrodes used for electrical measurements), providing extra information. Now the electrical and thermal measurements can be combined to yield improved information about the internal structure of the body.

  • Takashi Kako from University of Electro-Communications, Chofu-Tokyo, Japan, is an expert on resonances, and he will talk about their role in the formation of vowels in human speech. The related inverse problem is quite tricky: given a recording of a vowel sound, recover the shape of the vocal tract and the excitation signal arising from the vocal folds flapping against each other.

    Pictured are simplified vocal tract models for the five Japanese vowels: /a/, /i/, /u/, /e/, /o/.

  • Eero Saksman, University of Helsinki: Adaptive Markov chain Monte Carlo (MCMC) methods (joint with Johanna Tamminen and Heikki Haario). In Bayesian inversion, one often needs to compute high dimensional integrals (posterior mean). Due to the "curse of dimensionality" it is not a good idea to use a quadrature method.

    Instead, MCMC shoots plenty of points in the space, distributed according to the posterior probability. The average of the points is close to the integral. Now if the posterior probability has a weird shape, regular MCMC may not visit all corners of positive probability. Adaptive MCMC monitors the chain and modifies the search strategy on the fly, guiding the process to all relevant areas.