Parallel session 5
Thu, 09:00-11:00



M7-II: CURRENT DEVELOPMENTS IN TOMOGRAPHY: FROM THEORY TO ALGORITHMS (PART 2)

ORGANIZERS: Jurgen Frikel, Esther Klann, Todd Quinto

TALKS & SPEAKERS:

Inversion of the spherical means transform with centers lying on corner-like surfaces by reduction to the classical Radon transform
Leonid Kunyansky

Combining frequency-difference and ultrasound-modulated electrical impedance tomography
Bastian Harrach

Model-aware Newton-type regularization in electrical impedance tomography
Andreas Rieder

3D Image Reconstruction Algorithm for EIT Data Collected on Planar Electrode Arrays
Cristiana Sebu



M41-I: ADVANCES IN ELECTRICAL IMPEDANCE TOMOGRAPHY IMAGING: ALGORITHMS AND EXPERIMENTAL RESULTS (PART 1)

ORGANIZERS: Sarah Hamilton

TALKS & SPEAKERS:

Multispectral imaging methods for EIT
Emma Malone

Utilizing depth dependency in iterative EIT reconstruction
Henrik Garde

A D-bar algorithm with a priori information for 2-D electrical impedance imaging
Melody Dodd

3-D Electrical Impedance Imaging
Peter Muller



M6-I: RECENT ADVANCES IN THE THEORY OF REGULARIZATION METHODS (PART 1)

ORGANIZERS: Otmar Scherzer, Bernd Hofmann

TALKS & SPEAKERS:

Necessary Conditions for Variational Regularization
Dirk Lorenz

Singular Vectors for Nonlinear Regularization
Martin Burger

Regularization based on all-at-once formulations of inverse problems for PDEs
Barbara Kaltenbacher

Source conditions for non-smooth sparse regularisation
Markus Grasmair



M22: QUANTITATIVE ESTIMATES OF UNIQUE CONTINUATION AND APPLICATIONS TO INVERSE PROBLEMS

ORGANIZERS: Michele Di Cristo, Elisa Francini

TALKS & SPEAKERS:

A functional model of symmetric semibounded operator in inverse problems
Mikhail Belishev

Unique continuation for viscoelasticity equations
Gen Nakamura

Positive and negative results of the unique continuation property for the general second order elliptic system
Jenn-Nan Wang

Inverse boundary-value problems in an infinite slab with partial data
Kaloyan Marinov



M47-I: INVERSE PROBLEMS IN OPTICS (PART 1)

ORGANIZERS: Gang Bao, Peijun Li, Jun Zou

TALKS & SPEAKERS:

Near-Field Imaging via Inverse Scattering
Gang Bao
   ***CANCELLED***

Inverse Surface Scattering for Elastic Waves
Peijun Li

Inverse Problem for Period Media
Fioralba Cakoni

A multiscale model reduction method for wave propagation and its applications
Eric Chung

The two-dimensional direct and inverse scattering problems with generalized oblique derivative boundary condition
Jijun Liu



M36-I: OPTIMIZATION METHODS FOR SIGNAL AND IMAGE PROCESSING (PART 1)

ORGANIZERS: Ignace Loris, Marco Prato

TALKS & SPEAKERS:

Alternating Direction Approximate Newton Algorithm for Ill-conditioned inverse Problems
Maryam Yashtini

A convergent alternating-block iterative scheme for least-squares regularized blind deconvolution
Federica Porta

On the ergodic convergence rates of a first-order primal-dual algorithm
Thomas Pock

Scaled gradient projection method for linear system identification
Riccardo Zanella



M10-II: STOCHASTIC METHODS IN IMAGING (PART 2)

ORGANIZERS: Christian Clason, Kamil Kazimierski-Hentschel

TALKS & SPEAKERS:

Posterior Consistency and Convergence Rates for Bayesian Inversion with Hypoelliptic Operators
Hanne Kekkonen

Total variation image restoration with iterated conditional expectations
Cecile Louchet

Mixed noise models and their adaption to image data
Carola Schonlieb

Statistical inverse problems in fluorescence microscopy
Frank Werner



M42-I: INVERSE PROBLEMS IN LIFE SCIENCES (PART 1)

ORGANIZERS: Daniela Calvetti, Erkki Somersalo

TALKS & SPEAKERS:

On reconstruction of the dynamic tortuosity functions of poroelastic materials
Miao-Jung Yvonne Ou

Optimal Design of Non-equilibrium Experiments for Inverse Problems: Genetic Network Interrogation
H. Thomas Banks

Stochastic Reaction-Diffusion Modeling of Cellular Processes
Samuel Isaacson

A Bayesian method for identifying periods of latency in the phylogenetic history of HIV-1 within a host
Taina Immonen



M49-I: PLASMONICS AND CALR

ORGANIZERS: Petri Ola, Hyeonbae Kang

TALKS & SPEAKERS:

Spectral theory of Neumann-Poincaré operator and applications
Hyeonbae Kang

Anomalous resonance and cloaking: a review
Graeme Milton

Cloaking via anomalous localized resonance for doubly complementary media in the quasistatic regime
Hoai-Minh Nguyen

Plasmon resonances of nanoparticles
Eric Bonnetier



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.