Contributed Talks
Fri, 08:30-10:00


ORGANIZERS: Andreas Langer


Adaptive Regularization in Image Processing
Andreas Langer

Regularization approaches for quantitative Photoacoustic tomography using the radiative transfer equation
Adriano De Cezaro

Reconstructed Point Based Discretization Method for Image Reconstruction
Jun Qiu

A new alternating minimization algorithm for tomographic reconstruction in hydrokinetics experiments
Linghai Kong


ORGANIZERS: Christian Nittinger


Experimental estimation of local heat-transfer coefficient in coiled tubes with corrugated wall
Fabio Bozzoli

Analysis and numerical solution of the nonlinear evolutional inverse problem related to elastoplastic torsional equation
Salih Tatar

Magnetotelluric inversion with wavelet sparsity regularization
Christian Nittinger

Physics-based reconstruction of 3d instantaneous flow-fields from sparse velocity measurements
Jan Schneiders


ORGANIZERS: Fabien Caubet


Inverse problems related to space-time fractional diffusion equations
Suleyman Ulusoy

Microlocal analysis of restricted X-ray transforms of symmetric tensor fields in 3D Euclidean space
Rohit Kumar Mishra

Shape optimization methods for the Inverse Obstacle Problem
Fabien Caubet

The eigenvalues function and the inverse Sturm-Liouville problems
Tigran Harutyunyan


ORGANIZERS: Dominik Garmatter


Error estimates for exponentially ill-posed problems with impulsive noise
Claudia Konig

Coupling reduced basis methods and the Landweber method to solve inverse problems
Dominik Garmatter

On an inverse coefficient problem for hyperbolic equation with nonlocal conditions
Anar Rahimov

A Meshless Framework for Full Wave Inversion
Hebert Montegranario


ORGANIZERS: Dinh-Liem Nguyen


Recovery by finite number of measurements
Amin Boumenir

Prediction of nocturnal hypoglycemia by means of regularized ranking and collaborative filtration
Galyna Kriukova

On the numerical solution of a Cauchy problem for the Laplace equation in 3-dimensional annular domains by an integral equation method
B. Tomas Johansson

Imaging of inhomogeneities in an electromagnetic waveguide
Dinh-Liem Nguyen


ORGANIZERS: Mikael Kuusela


Regularization of Linear Ill-Posed Problems in Banach Lattices and its Applications to Diffusion Tensor Imaging
Yury Korolev

Determining White Noise Forcing From Eulerian Observations in the Navier-Stokes Equation
Viet Ha Hoang

Statistical Methods for Unfolding Elementary Particle Spectra at the Large Hadron Collider
Mikael Kuusela

A Sparse Coding Approach for Inverse Problem in Imaging via Self-Adaptive Probability Distribution
Xiaoyue Luo

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.