Parallel session 9
Fri, 13:30-15:30



M6-II: RECENT ADVANCES IN THE THEORY OF REGULARIZATION METHODS (PART 2)

ORGANIZERS: Otmar Scherzer, Bernd Hofmann

TALKS & SPEAKERS:

Effects of parameterization on the parameter estimation problems
Lingyun Qiu

Generalized Convergence Rates Results for Linear Inverse Problems in Hilbert Spaces
Peter Elbau

Reconstruction methods for the Inverse Medium Scattering Problem
Kamil Kazimierski-Hentschel

Autoconvolution in the characterization of ultrashort laser pulses with SD-SPIDER
Stephan Anzengruber



M33: INVERSE PROBLEMS WITH APPLICATIONS IN BIOLOGY

ORGANIZERS: Jan-Frederik Pietschmann, Matthias Schlottbom

TALKS & SPEAKERS:

Methods for Automatic Mitosis Detection and Tracking in Phase Contrast Images
Joana Grah

Cellular Force and Stress Reconstruction
Guido Vitale

Model selection for bacterial growth and division process
Marie Doumic Jauffret

Inverse Problems in Chemotaxis
Jan-Frederik Pietschmann



M21-II: RECONSTRUCTION METHODS FOR INVERSE PROBLEMS (PART 2)

ORGANIZERS: Masaru Ikehata, Jenn-Nan Wang

TALKS & SPEAKERS:

The equivalent mass density for the elastic scattering by many obstacles with error estimates and applications
Durga Prasad Challa

CGO solutions of anisotropic Maxwell's equations
Rulin Kuan

An efficient finite element method for grating profile reconstruction
Jiguang Sun

Subspace reconstruction algorithms for some severely ill-posed inverse problems
Kui Ren



M38-II: INVERSE BOUNDARY VALUE PROBLEMS FOR ELLIPTIC SYSTEMS (PART 2)

ORGANIZERS: Francis Chung, Mikko Salo

TALKS & SPEAKERS:

Coefficients identification problem for elasticity systems
Gen Nakamura

On partial data inverse problems for Maxwell equations
Petri Ola

Stable determination of an elastic inclusion by boundary measurements
Edi Rosset

On uniqueness of an inverse problem for the time harmonic Maxwell equations
Ting Zhou
   ***CANCELLED***



M16-II: EFFICIENT RECONSTRUCTION METHODS FOR ELECTRICAL IMPEDANCE TOMOGRAPHY AND INVERSE SCATTERING (PART 2)

ORGANIZERS: Roland Griesmaier, Nuutti Hyvonen

TALKS & SPEAKERS:

Construction of invisible conductivity perturbations for the point electrode model in EIT
Lucas Chesnel

Enhancing residual-based techniques with shape reconstruction features in EIT
Mach Nguyet Minh

Edge-enhancing reconstruction algorithm for three-dimensional electrical impedance tomography
Helle Majander

Exterior approach to inclusion detection in a parabolic inverse boundary value problem
Jeremi Darde



M39: QUANTITATIVE SOFT BIOLOGICAL TISSUES IMAGING

ORGANIZERS: Laurent Seppecher

TALKS & SPEAKERS:

Hybrid soft tissues imaging by mechanical perturbations
Laurent Seppecher

Computational and quantification challenges in high performance optoacoustic imaging
Daniel Razansky

Photoacoustic imaging with speckle illumination
Thomas Chaigne

Spectroscopic imaging of biological tissues
Laure Giovangigli



M31: SPECTRAL TOMOGRAPHY: MODELS, METHODS, AND APPLICATIONS

ORGANIZERS: Martin Andersen, Per Christian Hansen

TALKS & SPEAKERS:

Iterative Algorithms for Spectral Tomography
Martin Andersen

Spectral Tomography for Breast Imaging
James Nagy

Joint Reconstruction of Spectral CT Data via Constrained Total Nuclear Variation Minimization
David Rigie

Forward Model of Scatter Data Formation in Positron Emission Tomography and its Inversion
Ivan Kazantsev



M47-II: INVERSE PROBLEMS IN OPTICS (PART 2)

ORGANIZERS: Gang Bao, Peijun Li, Jun Zou

TALKS & SPEAKERS:

Quasi-conformal registration for multi-modality image reconstruction
Ronald Lui

Four-dimensional X-ray tomography for moving objects
Samuli Siltanen

Biosensing with metallic nanoparticles
Faouzi Triki

Travel Time Tomography with Partial Data
Gunther Uhlmann



CT4: IMAGING

ORGANIZERS: Federica Sciacchitano

TALKS & SPEAKERS:

Non-linear difference imaging approach to electrical impedance tomography with modeling errors
Dong Liu

Convex variational approach for restoring blurred images with Cauchy noise
Federica Sciacchitano

Fluorescence Microscopy: Deconvolution with Phase Retrieved Point Spread Function
Christina Brandt

Finite propagation speed in viscoelastic media
Jeong-Rock Yoon



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.