Abstract : This minisymposium addresses both theoretical and algorithmic aspects of inverse problems arising in tomography as well as their applications. We will bring together well established scientists and young researchers to provide a forum to discuss new ideas and developments in the field of applied inverse problems.
[04397] Perturbation of Surface Waves in Piezoelectric Media
Format : Talk at Waseda University
Author(s) :
Kazumi Tanuma (Gunma University)
Xiang Xu (Zhejiang University)
Gen Nakamura (Hokkaido University)
Abstract : We study Bleustein-Gulyaev (BG) waves which propagate along the surface of a homogeneous $C_6$ hexagonal piezoelectric half-space under the mechanically-free and electrically-closed condition at the surface. We prove stability of the BG waves, to investigate the perturbations of their phase velocity and polarization when a fully anisotropic perturbation is added to the hexagonal material constants. The inverse problem to obtain material information from measurements of BG waves will be discussed.
[04646] Quantitative Parameter Reconstruction from Optical Coherence Tomographic Data
Format : Talk at Waseda University
Author(s) :
Leopold Veselka (University of Vienna)
Abstract : We discuss the quantification of the refractive index from data obtained by optical coherence tomography - an imaging modality based on the interferometric measurement of back-scattered light. We consider samples with layered structure, where the refractive index as a function of depth is a piece-wise constant function. The applicability of the reconstruction method, where the refractive index is obtained layer-by-layer via least squares minimization, is verified by numerical examples for both simulated and experimental data.
This is a joint work with Peter Elbau (University of Vienna, Austria) and Leonidas Mindrinos (Agricultural University of Athens, Greece).
[04241] Landweber-Kaczmarz for full datacube modelling in Extragalactic Archaeology
Format : Talk at Waseda University
Author(s) :
Fabian Hinterer (JKU Linz)
Abstract : We consider the problem of reconstructing a galaxy’s stellar population distribution function from spectroscopy measurements. These quantities can be connected via the single-stellar population spectrum, resulting in a very large scale integral equation with a system structure. To solve this problem, we propose a projected Nesterov-Kaczmarz reconstruction (PNKR) method, which efficiently leverages the system structure and incorporates physical prior information such as smoothness and non-negativity constraints.
[03014] Principles and Examples of Magnetic Resonance Elastography for Distribution Measurement of Viscoelasticity
Format : Talk at Waseda University
Author(s) :
Mikio Suga (Chiba University)
Abstract : The mechanical property of a tissue is related to physiological and pathological states. Magnetic resonance elastography (MRE) is an imaging technique that can noninvasively measure the physical properties of biological soft tissues by using a magnetic resonance imaging system. Measuring the mechanical properties of tissues is expected to be helpful in diagnosing diseases such as hepatic fibrosis and cancer. In this minisymposium, I will talk about the principles and examples of MRE.
[04180] Inverse scattering technique for a defect in anisotropic plates
Format : Talk at Waseda University
Author(s) :
Takahiro SAITOH (Gunma University)
Abstract : In recent years, plates with anisotropic properties, such as CFRP, have been increasingly used in the engineering industry. In general, it is known that the elastic wave propagation is very complicated in anisotropic plates, due to the anisotropic properties and the generation of some types of wave modes between the incident wave and both upper and lower surfaces. In this study, the author proposes an inverse scattering technique for reconstructing a defect in anisotropic plates.
[03045] Source Reconstruction from Partial Boundary Data in Radiative Transport
Format : Talk at Waseda University
Author(s) :
Kamran Sadiq (Johann Radon Institute for Computational and Applied Mathematics (RICAM))
Abstract : This talk concerns the source reconstruction problem in a transport problem through an absorbing and scattering medium from boundary measurement data on an arc of the boundary. The method, specific to two dimensional domains, relies on Bukgheim’s theory of A-analytic maps and it is joint work with A. Tamasan (UCF) and H. Fujiwara (Kyoto U).
[03961] Numerical challenges to optical tomography by the stationary radiative transport equation
Format : Talk at Waseda University
Author(s) :
I-Kun Chen (National Taiwan University)
Hiroshi Fujiwara (Kyoto University)
Daisuke Kawagoe (Kyoto University)
Abstract : We discuss quantitative feasibility of optical tomography based on the stationary radiative transport equation which is a mathematical model of particle migration with absorption and scattering by medium. The key idea is the use of discontinuity of its solution induced by a proper boundary condition and discontinuous Galerkin methods. Numerical examples are exhibit to show a possibility of reconstruction of the attenuation coefficient without a priori information on the scattering kernel.
[04301] Inversion of the momenta X-ray transform of symmetric tensor fields in the plane.
Format : Online Talk on Zoom
Author(s) :
Alexandru Tamasan (University of Central Florida)
Kamran Sadiq (Johann Radon Institute for Computational and Applied Mathematics (RICAM))
David Omogbhe (University of Vienna)
Hiroshi Fujiwara (Kyoto University)
Abstract : The X-ray transform of symmetric tensor fields recovers the tensor field only up to a potential field. In 1994,
V. Sharafutdinov showed that augmenting the X-ray data with several momentum $X$-ray transforms establishes
uniqueness, with a most recent work (2022) showing stability of the inversion. In this talk, I will present a first reconstruction method, which stably recovers sufficiently smooth symmetric tensor fields compactly supported in the plane.
The method is based on the extension of Bukhgeim's theory to a system of A-analytic maps. This is joint work with H. Fujiwara, D. Omogbhe and K. Sadiq.
