Parallel session 7
Thu, 16:00-18:00



M24-I: MULTIFACETED PERSPECTIVE ON REGULARIZATION THEORY AND ITS APPLICATIONS (PART 1)

ORGANIZERS: Elena Resmerita, Stefan Kindermann

TALKS & SPEAKERS:

Regularization of operators with Poisson data
Federico Benvenuto

An Online Parameter Identification Method for time-dependent problems
Romana Boiger

Projective iterative methods for solving ill-posed problems under the tangential cone condition
Antonio Leitao

Regularization for inverse problems in anomalous diffusion
Bangti Jin



M30-I: IMAGING USING LIGHT: FROM THEORY TO APPLICATION (PART 1)

ORGANIZERS: Teresa Correia, Tanja Tarvainen

TALKS & SPEAKERS:

Mathematical modeling of OCT and PAT
Otmar Scherzer

Fast acquisition and reconstruction for fluorescence molecular tomography
Nicolas Ducros

Topological reduction of the inverse Born series
John Schotland

Recent advances in fluorescence molecular tomography image reconstruction
Teresa Correia



M45-I: INTEGRAL GEOMETRY (PART 1)

ORGANIZERS: Plamen Stefanov, Francois Monard

TALKS & SPEAKERS:

On the stability of the geodesic ray transform
Sean Holman

Applications of tensor and non-Abelian ray transforms
Bill Lionheart

Microlocal analysis of artifacts in limited data Radon transforms
Todd Quinto

The geodesic X-ray transform on Riemannian surfaces with conjugate points
Plamen Stefanov



M15-I: REGULARISATION TECHNIQUES FOR JOINT IMAGE RECONSTRUCTION PROBLEMS (PART 1)

ORGANIZERS: Simon Arridge, Martin Burger

TALKS & SPEAKERS:

Joint inversion using structural priors
Eldad Haber

Information Tomography
Stefano Pedemonte

In-vivo multi-contrast joint MR-PET image reconstruction: Initial findings in a clinical setting
Florian Knoll

Sparsity-based image reconstruction in electrical and electromagnetic tomography: experimental evaluation
Manuchehr Soleimani



M46-II: LEARNING SUBSPACES (PART 2)

ORGANIZERS: Massimo Fornasier, Valeriya Naumova

TALKS & SPEAKERS:

Active Subspaces in Theory and Practice
Paul Constantine

Spectral k-Support Norm Regularization
Massimiliano Pontil

Learning a Set by Kernel Methods
Ernesto De Vito

Local Dictionary Identification via Iterative Thresholding and K-means
Karin Schnass



M21-I: RECONSTRUCTION METHODS FOR INVERSE PROBLEMS (PART 1)

ORGANIZERS: Masaru Ikehata, Jenn-Nan Wang

TALKS & SPEAKERS:

The enclosure method for inverse obstacle scattering using a single electromagnetic wave in time dom
Masaru Ikehata

On reconstruction of a welding area by means of the enclosure method using a single measurement
Hiromichi Itou

Numerical analysis of the enclosure method for the heat equation in one-space dimension
Kiwoon Kwon

Reconstruction of penetrable obstacles in the anisotropic acoustic scattering
Yi-Hsuan Lin



M1-II: COMPUTATION OF INTERIOR TRANSMISSION EIGENVALUES (PART 2)

ORGANIZERS: Armin Lechleiter, Jiguang Sun

TALKS & SPEAKERS:

Computing Interior Eigenvalues from Far Field Data
Zixian Jiang

Error Estimates for the Finite Element Approximation of Transmission Eigenvalues
Peter Monk

On the Inside-Outside Duality for the Computation of Interior Transmission Eigenvalues for Anisotropic Media
Stefan Peters

A transmission eigenvalue problem with mixed boundary conditions for Maxwell's equations in half space
Virginia Selgas



M43-II: INVERSE PROBLEMS IN ATMOSPHERIC REMOTE SENSING (PART 2)

ORGANIZERS: Johanna Tamminen, Andreas Hilboll, Emily King

TALKS & SPEAKERS:

Markov Chain Monte Carlo Methods for Greenhouse Gas Measurements
Marko Laine

GOMOS satellite instrument: inverse problems and measurement highlights
Viktoria Sofieva

A Gradient-Based Reconstruction Method for Complex AO Systems
Daniela Saxenhuber

Finite Element-Wavelet Hybrid Algorithm (FEWHA) for Atmospheric Tomography
Mykhaylo Yudytskiy



CT3: OPTIMIZATION AND REGULARIZATION

ORGANIZERS: Sara Soltani

TALKS & SPEAKERS:

Tomographic Image Reconstruction Using Dictionary Priors
Sara Soltani

Fast voxel scoring for 6D X-ray Diffraction Tomography
Mirza Karamehmedovic

Numerical comparison of parameter choice rules using a new web toolbox
Reimo Palm

A new heuristic rule for choosing regularization parameter
Toomas Raus



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.