Parallel session 10
Fri, 16:00-18:00



M4: OPTIMIZATION APPROACHES FOR INVERSE PROBLEMS OF PARAMETER IDENTIFICATION

ORGANIZERS: Akhtar Khan, Christiane Tammer

TALKS & SPEAKERS:

Stability of Elastography Inverse Problem
Akhtar Khan

An Optimization Regularization Approach to Parameter Identification in Contact Problems
Joachim Gwinner

Optimization methods for Helmholtz problem
Victor Kovtunenko

Inverse Problems and Multiobjective Approximation
Christiane Tammer



M9: INVERSE PROBLEMS AND BIG DATA

ORGANIZERS: Mikko Kaasalainen

TALKS & SPEAKERS:

Big data in space
Mikko Kaasalainen

Radio tomography and experiment design
Sampsa Pursiainen

Next-generation forest models from ubiquitous laser scanning data
Pasi Raumonen

Data assimilation for weather - and further
Heikki Haario



M42-II: INVERSE PROBLEMS IN LIFE SCIENCES (PART 2)

ORGANIZERS: Daniela Calvetti, Erkki Somersalo

TALKS & SPEAKERS:

Parameter Estimation in Cardiovascular Modeling
Mette Olufsen

Inverse Problems for Structured Population Models
Jorge Zubelli

Hierarchical methods for parameter estimation in SPDE dynamics with application to disease Ecology
Luca Gerardo-Giorda

Model and solution reduction techniques for patient-specific parameter estimation in cardiovascular mathematics: failure and success
Huanhuan Yang



M18-II: IMAGING THROUGH COMPLEX MEDIA (PART 2)

ORGANIZERS: Josselin Garnier, Knut Solna

TALKS & SPEAKERS:

Waves and imaging in random media
Josselin Garnier

A mathematical theory of super-resolution by using Helmholtz resonators
Hai Zhang

Signal to Noise Ratio analysis in virtual source array imaging
Chrysoula Tsogka



M35: INVERSE PROBLEMS FOR HYPERBOLIC PDES

ORGANIZERS: Lauri Oksanen

TALKS & SPEAKERS:

The determination of the black hole by boundary measurements
Gregory Eskin

Inverse problems in bistatic SAR with different speeds
Raluca Felea

A Traveltime Inverse Problem in Spacetime
Yang Yang

Multiwave Tomography in closed domains
Plamen Stefanov



M5-II: AUTOCONVOLUTION AND RELATED NONLINEAR ILL-POSED PROBLEMS (PART 2)

ORGANIZERS: Bernd Hofmann, Jens Flemming

TALKS & SPEAKERS:

Multiscale support vector approach for solving integral equations
Shuai Lu

New results in SD-SPIDER reconstruction via autoconvolution
Steven Burger

The quadratic structure of autoconvolution problems
Jens Flemming

A stochastic convergence analysis for nonlinear operator equations with emphasis on the Autoconvolution problem
Daniel Gerth



M15-II: REGULARISATION TECHNIQUES FOR JOINT IMAGE RECONSTRUCTION PROBLEMS (PART 2)

ORGANIZERS: Simon Arridge, Martin Burger

TALKS & SPEAKERS:

Laminar CT reconstruction via sparsity constrained debluring
Thomas Blumensath

Joint reconstruction of PET-MRI by exploiting structural similarity
Matthias Ehrhardt

Exploiting Joint Gradient Sparsity in Multi-Channel Image Reconstruction
Eva-Maria Brinkmann

Bi-modal image reconstruction using the Mumford-Shah model with an application to PET-MRI
Thomas Page



M29: PRIORS AND SPDES

ORGANIZERS: Lassi Roininen, Simo Sarkka

TALKS & SPEAKERS:

Levy alpha-stable priors for Bayesian inversion
Lassi Roininen

Evolution equation representation of regularization in dynamic inverse problems
Simo Sarkka

Meshes, hyperparameters and priors: Practical aspects of Bayesian inverse problems with SPDE priors
Daniel Simpson

Probabilistic parcellation of whole-brain fMRI using Chinese restaurant and Gaussian process priors
Pasi Jylanki



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.