Parallel session 3
Tue, 13:30-15:30



M2-II: MODELS AND METHODS FOR HYPERSPECTRAL IMAGING

ORGANIZERS: Martin Burger, Thomas Schuster

TALKS & SPEAKERS:

Using local sparsity in hyperspectral imaging
Pia Heins

Total generalized variation for vector- and tensor-valued data and applications in medical imaging
Kristian Bredies

Coupled hyperspectral total variation regularization
Michael Moller

Application of preprocessing methods on hyperspectral images from different spectral ranges
Martin Montag



M34-II: RECENT TRENDS IN HYBRID TOMOGRAPHY (PART 2)

ORGANIZERS: Simon Arridge, Marta Betcke, Kim Knudsen

TALKS & SPEAKERS:

Stability for Current Density Impedance Imaging
Carlos Montalto

Reconstructions in Photoacoustics with Variable Sound Speed
Otmar Scherzer

Mathematical Modeling in Full Field Optical Coherence Elastography
Pierre Millien

Inverse Transport and Acousto-Optic Imaging
John Schotland



M11-II: ANALYTICAL ASPECTS OF REGULARISATION: HIGHER-ORDER AND CURVATURE-BASED APPROACHES AND FURTHER TOPICS (PART 2)

ORGANIZERS: Tuomo Valkonen

TALKS & SPEAKERS:

How generalised singular vectors can help to develop new regularisation methods
Martin Benning

Imaging with Kantorovich-Rubinstein discrepancy
Dirk Lorenz

Resolving the white noise paradox in the regularisation of inverse problems
Hanne Kekkonen

Nonlinear Diffusions of Image Processing and Their Analysis
Patrick Guidotti



M13-II: DISCRETIZATION OF INVERSE PROBLEMS IN BANACH SPACES (PART 2)

ORGANIZERS: Barbara Kaltenbacher, Christiane Poschl

TALKS & SPEAKERS:

On self-regularization of illposed problems in Banach spaces by least squares and least error method
Urve Kangro

A posteriori choice of the dimension in self-regularization of ill-posed problems by the collocation method
Uno Hamarik

Recovering delta-peak solutions for inverse problems by image-side discretization in Radon space
Kristian Bredies

Mesh adaptivity for the discretization of sparse elliptic control problems
Konstantin Pieper



M20-II: STABILITY ESTIMATES FOR INVERSE PROBLEMS (PART 2)

ORGANIZERS: Victor Isakov, Jenn-Nan Wang

TALKS & SPEAKERS:

The stable reconstruction of acoustic and electromagnetic radiation regions at the radiating structure
Nicolas Valdivia

Increasing stability phenomena for the Maxwell equations
Ru-Yu Lai

Obstacle scattering problems in the high frequency asymptotics
Luca Rondi

Stability estimates for multi-frequency inverse scattering problems
Faouzi Triki



M48-II: RECENT DEVELOPMENTS ON NUMERICAL INVERSE SCATTERING PROBLEMS (PART 2)

ORGANIZERS: Jingzhi Li, Hongyu Liu, Jun Zou

TALKS & SPEAKERS:

On Spectral Analysis and A Novel Algorithm for Transmission Eigenvalue Problems
Jijun Liu

An Adaptive Finite Element Method for Reconstruction of the Robin Coefficient
Yifeng Xu

Reconstruction of an impedance cylinder at oblique incidence from the far-field data
Haibing Wang



M43-I: INVERSE PROBLEMS IN ATMOSPHERIC REMOTE SENSING (PART 1)

ORGANIZERS: Johanna Tamminen, Andreas Hilboll, Emily King

TALKS & SPEAKERS:

Observational Requirements for Next-Generation Cloud Remote Sensing Systems: A Bayesian Persective
Derek Posselt

CO2 Retrievals for the OCO-2 Instrument: Full MCMC Exploration Using a Surrogate Forward-Model
Jenny Brynjarsdottir

Dimension Reduction in Bayesian Inverse Problems Applied to Atmospheric Remote Sensing
Antti Solonen

Data Fusion for Massive, Remote Sensing Data Sets
Amy Braverman



M46-I: LEARNING SUBSPACES (PART 1)

ORGANIZERS: Massimo Fornasier, Valeriya Naumova

TALKS & SPEAKERS:

Geometric Methods for the Approximation of High-dimensional Dynamical Systems
Mauro Maggioni

Piecewise Data Representation to Learn Manifold and Measures
Lorenzo Rosasco

Generalization Performance of Multi-Task Subspace Learning
Andreas Maurer

Factor Models for High-dimensional Time Series
Christine De Mol

On the Convergence Rate and Some Applications of Regularised Ranking Algorithms
Sergei Pereverzyev



M8-II: CURRENT DEVELOPMENTS IN TOMOGRAPHY: FROM ALGORITHMS TO APPLICATIONS (PART 2)

ORGANIZERS: Jurgen Frikel, Esther Klann, Todd Quinto

TALKS & SPEAKERS:

X-ray Tensor Tomography: reconstructing sub-pixel X-ray scattering data
Tobias Lasser

Assessing undersampling levels in sparsity-regularized X-ray CT
Jakob Sauer Jorgensen

Reconstruction methods for atmospheric tomography
Ronny Ramlau

Inversion of the Broken Ray transform
Alexander Katsevich



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.