Parallel session 2
Mon, 16:00-18:00



M2-I: MODELS AND METHODS FOR HYPERSPECTRAL IMAGING

ORGANIZERS: Martin Burger, Thomas Schuster

TALKS & SPEAKERS:

Compressed sensing in mass spectrometry imaging
Andreas Bartels

Statistical estimation in a parametric regression model for hyperspectral images
Ulrike Mayer

Cancer ID - inverse problems for the multidimensional analysis of tumor cells
Christoph Brune

Minimizing the regularized l1-norm via Bregman projections and subspace methods
Frederik Heber



M37-I: INVERSE PROBLEMS IN NON-DESTRUCTIVE TESTING (PART 1)

ORGANIZERS: Habib Ammari, Aku Seppanen, Manuchehr Soleimani

TALKS & SPEAKERS:

Electrical impedance tomography for detection of damage and monitoring moisture flow in Concrete
Aku Seppanen

Electrical and Electromagnetic Tomography Methods for NDE
Manuchehr Soleimani

Electrical impedance spectroscopic imaging for detecting cracks and reinforcing bars in concrete structures
Tingting Zhang

Detection and identification of targets from eddy current data
Darko Volkov



M11-I: ANALYTICAL ASPECTS OF REGULARISATION: HIGHER-ORDER AND CURVATURE-BASED APPROACHES AND FURTHER TOPICS (PART 1)

ORGANIZERS: Tuomo Valkonen

TALKS & SPEAKERS:

Convex approximation of Euler's elastica via functional lifting: More feasible than expected?
Benedikt Wirth

Some regularity questions regarding a generalized Willmore functional
Simon Masnou

Structure of solutions of the TGV regularisation problem
Kostas Papafitsoros

The jump set under geometric regularisation
Tuomo Valkonen



M20-I: STABILITY ESTIMATES FOR INVERSE PROBLEMS (PART 1)

ORGANIZERS: Victor Isakov, Jenn-Nan Wang

TALKS & SPEAKERS:

Size estimates in inverse problems
Michele Di Cristo

A stability result for quantitative photoacoustic tomography
Elisa Francini

Stability of the Calderon problem in admissible geometries
Pedro Caro

The stability for the inverse source problem with multi-frequency
Jin Cheng



M44: QUALITATIVE METHODS FOR SOLVING INVERSE PROBLEMS

ORGANIZERS: Faouzi Triki, Eric Bonnetier

TALKS & SPEAKERS:

How to use tools from control theory to solve some inverse problems?
Mourad Choulli
   ***CANCELLED***

An Inverse Problem for the Helmhotz Equation in a Layered Media
Matias Courdurier

Well-posedness and limiting absorption principle for the Helmholtz equation with sign changing coefficients
Hoai-Minh Nguyen

New numerical results for the Gel'fand-Calderon problem
Matteo Santacesaria



M8-I: CURRENT DEVELOPMENTS IN TOMOGRAPHY: FROM ALGORITHMS TO APPLICATIONS (PART 1)

ORGANIZERS: Jurgen Frikel, Esther Klann, Todd Quinto

TALKS & SPEAKERS:

A weighted wavelet method for region of interest tomography
Esther Klann

Joint reconstruction and segmentation of tomographic data using the Potts model
Martin Storath

Detectable singularities in time-dependent tomographic imaging
Bernadette Hahn

X-ray tomography of dynamic objects using level sets
Samuli Siltanen



M25: EFFICIENT METHODS FOR LARGE-SCALE INVERSE PROBLEMS IN IMAGING

ORGANIZERS: Julianne Chung, Silvia Gazzola

TALKS & SPEAKERS:

Sparse reconstruction by flexible Krylov methods
Silvia Gazzola

Generalized Krylov Subspace Methods for lp - lq Minimization
Lothar Reichel

Total variation based exact two-phase method for impulse noise removal
Yiqiu Dong

Regularization methods for image reconstruction in 3D limited angle tomography
Elena Piccolomini



M32-I: BAYESIAN COMPUTATION

ORGANIZERS: Felix Lucka

TALKS & SPEAKERS:

Recent Advances in Bayesian Inference for Inverse Problems
Felix Lucka

Bayesian Framework for the Detection of Sharp Transitions
Iryna Sivak

Likelihood-informed Dimension Reduction in Nonlinear Inverse Problems
Youssef Marzouk

Where Bayes meets Krylov: Bayesian iterative linear solvers for inverse problems
Daniela Calvetti



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.