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BEGIN:VEVENT
SUMMARY:Multiscale approaches for removing multiplicative noise
DTSTART;VALUE=DATE-TIME:20230706T081000Z
DTEND;VALUE=DATE-TIME:20230706T083500Z
DTSTAMP;VALUE=DATE-TIME:20240304T071244Z
UID:indico-contribution-201-1469@conference2.aau.at
DESCRIPTION:Speakers: Elena Resmerita (MATH)\nThis work adapts a variety o
f both classical and new multiplicative noise removing models to the multi
scale hierarchical decomposition form\, following the idea of a seminal pa
per from 2004. Well-definedness and convergence properties are provided fo
r the proposed methods\, as well as comprehensive numerical experiments an
d comparisons.\nThis is joint work with Joel Barnett\, Wen Li and Luminita
Vese.\n\nhttps://conference2.aau.at/event/201/contributions/1469/
LOCATION:University of Klagenfurt HS 3
URL:https://conference2.aau.at/event/201/contributions/1469/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On solving the inverse problem of diffractive tensor tomography vi
a a transport equation
DTSTART;VALUE=DATE-TIME:20230705T101000Z
DTEND;VALUE=DATE-TIME:20230705T103500Z
DTSTAMP;VALUE=DATE-TIME:20240304T071244Z
UID:indico-contribution-201-1432@conference2.aau.at
DESCRIPTION:Speakers: Lukas Vierus (Saarland University)\nThe author discu
sses a method for dynamic tensor field tomography\, which involves recover
ing a tensor field from its longitudinal ray transform in an inhomogeneous
medium. The refractive index of the medium generates the Riemannian metri
c in the domain\, and the goal is to solve the inverse source problem for
the associated transport equation. While there are many results for recove
ring tensor fields in a static Euclidean setting\, there are few inversion
formulas and algorithms for general Riemannian metrics and time-dependent
tensor fields. Tensor field tomography is equivalent to an inverse source
problem for a transport equation\, with the ray transform as given bounda
ry data. In the dynamic case\, the same approach can be used. To ensure th
e forward mappings are well-defined\, existence and uniqueness for the tra
nsport equations must be proven. Unfortunately\, the bilinear forms of the
weak formulations do not satisfy the coercivity condition\, so viscosity
solutions are used instead. The author provides numerical evidence that th
e viscosity solution solves the original transport equation when the visco
sity term is zero. Additionally\, numerical experiments for the static cas
e are discussed. It turns out that the adjoint mapping can also be express
ed as solution of a transport equation and be solved by the method of char
acteristics. Numerical results for the reconstruction of stationary fields
are given.\n\nhttps://conference2.aau.at/event/201/contributions/1432/
LOCATION:University of Klagenfurt HS 3
URL:https://conference2.aau.at/event/201/contributions/1432/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nonlinear impedance boundary conditions in inverse obstacle scatte
ring
DTSTART;VALUE=DATE-TIME:20230707T083500Z
DTEND;VALUE=DATE-TIME:20230707T090000Z
DTSTAMP;VALUE=DATE-TIME:20240304T071244Z
UID:indico-contribution-201-1431@conference2.aau.at
DESCRIPTION:Speakers: Leonie Fink ()\nNonlinear impedance boundary conditi
ons in acoustic scattering are used as a model for perfectly conducting ob
jects coated with a thin layer of a nonlinear medium. We consider a scatte
ring problem for the Helmholtz equation with a nonlinear impedance boundar
y condition of the form $$\n\\frac{\\partial u}{\\partial \\nu} + ik\\lamb
da u = g(\\cdot\,u) \\quad \\text{on} \\ \\ \\partial D\,\n$$ where $\\nu$
denotes the unit normal vector\, $\\lambda \\in L^{\\infty}(\\partial D)$
is a complex-valued impedance function\, and $g: \\partial D \\times \\ma
thbb{C} \\to \\mathbb{C}$ gives an additional nonlinear term with respect
to the total field $u$. The contributed talk is devoted to the well-posedn
ess of the direct problem\, the determination of the domain derivative\, a
nd the inverse problem\, which consists in reconstructing the shape of the
scattering object from given far field data. Numerical results are presen
ted relying on an all-at-once regularized Newton-type method based on the
linearization of the forward problem and of the domain-to-far-field operat
or.\n\nhttps://conference2.aau.at/event/201/contributions/1431/
LOCATION:University of Klagenfurt HS 2
URL:https://conference2.aau.at/event/201/contributions/1431/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A paraxial approach for the inverse problem of vibroacoustic imagi
ng in frequency domain
DTSTART;VALUE=DATE-TIME:20230706T100000Z
DTEND;VALUE=DATE-TIME:20230706T102500Z
DTSTAMP;VALUE=DATE-TIME:20240304T071244Z
UID:indico-contribution-201-1467@conference2.aau.at
DESCRIPTION:Speakers: Teresa Rauscher ()\nVibroacoustic imaging by means o
f ultrasound is an imaging method that was developed to achieve higher res
olutions by sending in high frequency waves and making use of the differen
ce frequency to avoid the drawbacks of scattering and stronger attenuation
at high frequencies. We make use of a paraxial approach for the directive
beams and arrive at a system of PDEs that involves space dependent parame
ters. Reconstructing these parameters yields a spatial image of the region
of interest. In this talk\, we will deal with the modeling and inverse pr
oblem for vibroacoustic imaging.\n\nhttps://conference2.aau.at/event/201/c
ontributions/1467/
LOCATION:University of Klagenfurt HS 3
URL:https://conference2.aau.at/event/201/contributions/1467/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Determination of nonlinear local Material Properties using an Inve
rse Scheme
DTSTART;VALUE=DATE-TIME:20230705T143500Z
DTEND;VALUE=DATE-TIME:20230705T150000Z
DTSTAMP;VALUE=DATE-TIME:20240304T071244Z
UID:indico-contribution-201-1436@conference2.aau.at
DESCRIPTION:Speakers: Andreas Gschwentner (Institute of Fundamentals and T
heory in Electrical Engineering\, TU Graz)\nThe precise knowledge of the m
aterial properties is of utmost importance for motor manufacturers to desi
gn and develop highly efficient machines. However\, due to different manuf
acturing processes\, these material properties can vary greatly locally an
d the assumption of homogenized global material parameters is no longer fe
asible for the development process. The goal of our research project is to
precisely determine these local magnetic material properties using a comb
ined approach of measurements\, numerical simulations and the applications
of inverse methods. In this work\, we focus on the identification of the
local nonlinear permeabilities of electrical sheets considering cutting ed
ge effects. In doing so\, the electrical sheets are divided into subregion
s\, each assigned with a nonlinear magnetic material model. Furthermore\,
we generate the measured data by forward simulations solving the magnetic
field for the magneto-static case by applying the finite element (FE) meth
od and overlay these data with a Gaussian white noise. Based on the genera
ted data\, we apply our inverse scheme on the simulation model to determin
e the parameters of the nonlinear material model. To ensure solvability\,
a Tikhonov regularization with a prior information for the parameter is co
nsidered. The accuracy and convergency of our approach is investigated.\n\
nhttps://conference2.aau.at/event/201/contributions/1436/
LOCATION:University of Klagenfurt HS 3
URL:https://conference2.aau.at/event/201/contributions/1436/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Comparison of the Multiscale Hierarchical Decomposition Method and
generalized Tikhonov regularization
DTSTART;VALUE=DATE-TIME:20230705T084500Z
DTEND;VALUE=DATE-TIME:20230705T091000Z
DTSTAMP;VALUE=DATE-TIME:20240304T071244Z
UID:indico-contribution-201-1465@conference2.aau.at
DESCRIPTION:Speakers: Tobias Wolf ()\nThe Multiscale Hierarchical Decompos
ition Method (MHDM) is a popular method originating from mathematical imag
ing. In its original context\, it is very well suited to recover approxima
tions with fine details from blurred and noise-corrupted images. The main
idea is to iteratively decompose an image into a cartoon and a texture par
t at different scales. We consider the algorithm in a more general framewo
rk\, allowing one to apply it to a wider variety of problems. In this talk
\, we focus on comparing the MHDM to generalized Tikhonov regularization w
ith seminorm regularizers. We propose a necessary and sufficient condition
for the iterates of the MHDM to coincide with the minimizers of the Tikho
nov regularization. We illustrate the result on finite dimensional $\\ell^
1$ regularization and one-dimensional total variation denoising.\nJoint wo
rk with Elena Resmerita and Stefan Kindermann.\n\nhttps://conference2.aau.
at/event/201/contributions/1465/
LOCATION:University of Klagenfurt HS 3
URL:https://conference2.aau.at/event/201/contributions/1465/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Uncertainty Quantification of Inclusion Boundaries
DTSTART;VALUE=DATE-TIME:20230705T071000Z
DTEND;VALUE=DATE-TIME:20230705T080000Z
DTSTAMP;VALUE=DATE-TIME:20240304T071244Z
UID:indico-contribution-201-1457@conference2.aau.at
DESCRIPTION:Speakers: Yiqiu Dong (Technical University of Denmar)\nCompute
d tomography (CT) imaging is the task of reconstructing a positive attenua
tion field (in the form of an image) from a finite number of projections (
e.g.\, sinograms). CT reconstruction is often followed by an image segment
ation step to partition the image into piecewise smooth/constant regions.
The boundaries between such regions often carry valuable information.\n\nI
n this talk\, we will describe a Bayesian framework for reconstructing the
boundaries of piecewise constant regions in the CT problem in an infinite
-dimensional setting. Since the regularity of boundaries carries crucial i
nformation in many inverse problem applications\, e.g.\, in medical imagin
g for identifying malignant tissues or in the analysis of electroencephalo
gram for epileptic patients\, we characterize the regularity of the bounda
ry by means of its fractional differentiability. The proposed Bayesian for
mulation has a hierarchical structure\, which simultaneously estimates the
boundary and its regularity. In addition\, we quantify the uncertainties
in the estimates.\n\nOur approach is goal oriented\, meaning that we direc
tly detect the discontinuities from the data\, instead of reconstructing t
he entire image. This drastically reduces the dimension of the problem\, w
hich makes the application of Markov Chain Monte Carlo (MCMC) methods feas
ible.\n\nWe will show that the proposed method provides an excellent platf
orm for challenging X-ray CT scenarios (e.g.\, in case of noisy data\, lim
ited angle\, or sparse angle imaging). Furthermore\, this framework can be
extended to reconstruct 2D surfaces\, track the changes of the boundaries
\, and handle other types of noise.\nThis work has been published or submi
tted\, see [1\, 2].\n\n(joint work with Babak M. Afkham\, Nicolai A. Riis\
, Per Christian Hansen)\n\nReferences\n[1] B. M. Afkham\, Y. Dong\, P. C.
Hansen\, Uncertainty Quantification of Inclusion Boundaries in the Context
of X-Ray Tomography\, SIAM Journal on Uncertainty Quantification 11 (2023
)\, 31-61.\n[2] B. M. Afkham\, N. A. Riis\, Y. Dong\, P. C. Hansen\, Infer
ring Features with Uncertain Roughness\, Submitted\, http://arxiv.org/abs/
2305.04608.\n\nhttps://conference2.aau.at/event/201/contributions/1457/
LOCATION:University of Klagenfurt HS 3
URL:https://conference2.aau.at/event/201/contributions/1457/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stability of Bayesian Optimal Experimental Design in Inverse Probl
ems
DTSTART;VALUE=DATE-TIME:20230705T120000Z
DTEND;VALUE=DATE-TIME:20230705T125000Z
DTSTAMP;VALUE=DATE-TIME:20240304T071244Z
UID:indico-contribution-201-1464@conference2.aau.at
DESCRIPTION:Speakers: Tapio Helin (LUT University\, Finland)\nWe study the
stability properties of the expected utility function in Bayesian optimal
experimental design. We provide a framework for this problem in the case
of expected information gain criterion in an infinite-dimensional setting\
, where we obtain the convergence of the expected utility with respect to
perturbations. To make the problem more concrete we demonstrate that non-l
inear Bayesian inverse problems with Gaussian likelihood satisfy necessary
assumptions in our theory. Some numerical simulations with different exam
ples are explored.\n\nhttps://conference2.aau.at/event/201/contributions/1
464/
LOCATION:University of Klagenfurt HS 3
URL:https://conference2.aau.at/event/201/contributions/1464/
END:VEVENT
BEGIN:VEVENT
SUMMARY:The topological derivative as an imaging tool for object detection
DTSTART;VALUE=DATE-TIME:20230707T070000Z
DTEND;VALUE=DATE-TIME:20230707T075000Z
DTSTAMP;VALUE=DATE-TIME:20240304T071244Z
UID:indico-contribution-201-1461@conference2.aau.at
DESCRIPTION:Speakers: María-Luisa Rapún (Universidad Politécnica de Mad
rid)\nDetecting defects embedded in a medium is a problem of paramount int
erest in a variety of fields\, including medical imaging\, non-destructive
testing of materials and geophysical exploration. \n\nIn this talk we pre
sent numerical methods based on topological derivative computations for th
e detection of multiple objects. The method provides an indicator function
capable of classifying each point in the region of interest as belonging
to the background medium or to an object\, without any a priori assumption
about the number\, size\, shape\, or location of the objects. \nThe perfo
rmance of the method in different applications\, including acoustic\, elec
tromagnetic\, and thermographic inspection will be shown.\n\nhttps://confe
rence2.aau.at/event/201/contributions/1461/
LOCATION:University of Klagenfurt HS 2
URL:https://conference2.aau.at/event/201/contributions/1461/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Towards optimal sensor placement for sparse inverse problems
DTSTART;VALUE=DATE-TIME:20230707T092500Z
DTEND;VALUE=DATE-TIME:20230707T095000Z
DTSTAMP;VALUE=DATE-TIME:20240304T071244Z
UID:indico-contribution-201-1459@conference2.aau.at
DESCRIPTION:Speakers: Phuoc Truong Huynh ()\nIn this talk\, we study param
eter identification problems from a finite number of measurements under a
sparsity assumption. Since the data is contaminated by Gaussian noise\, a
statistical framework for its recovery is considered. It relies on two mai
n ingredients\, first\, a convex but nonsmooth Tikhonov point estimator ov
er the space of Radon measures and\, second\, a suitable mean-squared erro
r based on its Hellinger-Kantorovich (H-K) distance to the ground truth.\n
\nAssuming standard non-degenerate source conditions as well as applying c
areful linearization arguments\, we derive a sharp upper bound for the H-K
distance between the aforementioned ground truth and an estimator. On the
one hand\, this allows to derive asymptotic convergence results for the m
ean-squared error\, which is later used as a crucial tool for sensor place
ment problem. Finally\, we present some numerical results to illustrate ou
r theory.\n\nThis is a joint work with Konstantin Pieper and Daniel Walter
.\n\nhttps://conference2.aau.at/event/201/contributions/1459/
LOCATION:University of Klagenfurt HS 2
URL:https://conference2.aau.at/event/201/contributions/1459/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Multiharmonic expansions for nonlinearity identification in wave t
ype equations
DTSTART;VALUE=DATE-TIME:20230706T123500Z
DTEND;VALUE=DATE-TIME:20230706T130000Z
DTSTAMP;VALUE=DATE-TIME:20240304T071244Z
UID:indico-contribution-201-1458@conference2.aau.at
DESCRIPTION:Speakers: Barbara Kaltenbacher (MATH)\nWe consider an undeterm
ined coefficient inverse problem for a nonlinear partial differential equa
tion occuring in high intensity ultrasound propagation as used in acoustic
tomography.\nIn particular\, we investigate the recovery of the nonlinear
ity coefficient commonly labeled as $B/A$ in the literature\, which is par
t of a space dependent coefficient $\\kappa$ in the Westervelt equation g
overning nonlinear acoustics.\nCorresponding to the typical measurement se
tup\, the overposed data consists of time trace measurements on some zero
or one dimensional set $\\Sigma$ representing the receiving transducer arr
ay.\nIn this talk\, we will show some recent results pertaining to the for
mulation of this problem in frequency domain and numerical reconstruction
of piecewise constant coefficients in two space dimensions.\nThis is joint
work with Bill Rundell\, Texas A&M University.\n\nhttps://conference2.aau
.at/event/201/contributions/1458/
LOCATION:University of Klagenfurt HS 3
URL:https://conference2.aau.at/event/201/contributions/1458/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Inexact proximal Langevin sampling
DTSTART;VALUE=DATE-TIME:20230705T131000Z
DTEND;VALUE=DATE-TIME:20230705T133500Z
DTSTAMP;VALUE=DATE-TIME:20240304T071244Z
UID:indico-contribution-201-1440@conference2.aau.at
DESCRIPTION:Speakers: Lorenz Kuger (FAU Erlangen-Nürnberg & DESY Hamburg)
\nIn order to solve tasks like uncertainty quantification or hypothesis te
sts in Bayesian imaging inverse problems that go beyond the computation of
point estimates\, we have to draw samples from the posterior distribution
. For log-concave but usually high-dimensional posteriors\, Markov chain M
onte Carlo methods based on time discretizations of Langevin diffusion are
a popular tool. If the potential defining the distribution is non-smooth\
, as is the case for many relevant imaging problems\, these discretization
s are usually of an implicit form. This leads to Langevin sampling algorit
hms that require the evaluation of proximal operators\, which is\, for som
e of the potentials relevant in imaging problems\, only possible approxima
tely using an iterative scheme. We investigate the behaviour of a proximal
Langevin algorithm under the presence of errors in the evaluation of the
proximal mappings. We generalize existing non-asymptotic and asymptotic co
nvergence results of the exact algorithm to our inexact setting and quanti
fy the additional bias between the target and the algorithm's stationary d
istribution due to the errors. We show that the additional bias stays boun
ded for bounded errors and converges to zero for decaying errors in a stro
ngly convex setting. We show numerical results where we apply the inexact
algorithm to sample from the posterior of typical imaging inverse problems
in which we can only approximate the proximal operator by an iterative sc
heme.\n\nhttps://conference2.aau.at/event/201/contributions/1440/
LOCATION:University of Klagenfurt HS 3
URL:https://conference2.aau.at/event/201/contributions/1440/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the jump set of minimizers of scalar and vectorial Total-Variat
ion based regularization problems
DTSTART;VALUE=DATE-TIME:20230706T070000Z
DTEND;VALUE=DATE-TIME:20230706T075000Z
DTSTAMP;VALUE=DATE-TIME:20240304T071244Z
UID:indico-contribution-201-1456@conference2.aau.at
DESCRIPTION:Speakers: Antonin Chambolle (CEREMADE\, CNRS\, Université Par
is-Dauphine (PSL))\nIt has been shown a long time ago that the discontinui
ty set of the solution of a denoising problem by total variation minimizat
ion ("Rudin-Osher-Fatemi") is a subset of the discontinuity set of the ori
ginal data\, if smooth enough. In this talk\, I will review the techniques
used in the scalar setting\, a variant developed by T. Valkonen which in
theory addresses more cases (including vectorial)\, and a much simpler app
roach\, developed in collaboration with M. Łasica (Warsaw) and inspired b
y T. Valkonen's techniques\, yet which extends his results to even more ca
ses.\n\nhttps://conference2.aau.at/event/201/contributions/1456/
LOCATION:University of Klagenfurt HS 3
URL:https://conference2.aau.at/event/201/contributions/1456/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Acoustic Cavitation using Resonating Micro-Bubbles. Analysis in th
e Time-Domain
DTSTART;VALUE=DATE-TIME:20230706T090000Z
DTEND;VALUE=DATE-TIME:20230706T092500Z
DTSTAMP;VALUE=DATE-TIME:20240304T071244Z
UID:indico-contribution-201-1445@conference2.aau.at
DESCRIPTION:Speakers: Arpan Mukherjee (Johann Radon Institute (RICAM)\, Au
strian Academy of Sciences)\nWe study the time-domain acoustic wave propag
ation in the presence of a micro-bubble. This micro-bubble is characterize
d by a mass density and bulk modulus which are both very small as compared
to the ones of the uniform and homogeneous background medium. The goal is
to estimate the amount of pressure that is created very near (at a distan
ce proportional to the radius of the bubble) to the bubble. We show that\,
at that small distance\, the dominating field is reminiscent to the wave
created by a point-like obstacle modeled formally by a Dirac-like heteroge
neity with support at the location of the bubble and the contrast between
the bubble and background material as the scattering coefficient. As a con
clusion\, we can tune the bubbles material properties so that the pressure
near it reaches a desired amount. Such design might be useful in the purp
ose of acoustic cavitation where one needs enough\, but not too much\, pre
ssure to eliminate unwanted anomalies. The mathematical analysis is done u
sing time-domain integral equations and asymptotic analysis techniques. A
well known feature here is that the contrasting scales between the bubble
and the background generate resonances (mainly the Minnaert one) in the ti
me-harmonic regime. Such critical scales\, and the generated resonances\,
are also reflected in the time-domain estimation of the acoustic wave. In
particular\, reaching the desired amount of pressure near the location of
the bubble is possible only with such resonating bubbles.\n\nKey Words. Ti
me-Domain Acoustic Scattering\, Contrasting Media\, Bubbles\, Asymptotic
Analysis\, Retarded Layer and Volume Potentials\, Lippmann–Schwinger equ
ation.\n\nhttps://conference2.aau.at/event/201/contributions/1445/
LOCATION:University of Klagenfurt HS 3
URL:https://conference2.aau.at/event/201/contributions/1445/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Recovering both the wave speed and the source function in a time-d
omain wave equation by injecting high contrast bubbles
DTSTART;VALUE=DATE-TIME:20230706T083500Z
DTEND;VALUE=DATE-TIME:20230706T090000Z
DTSTAMP;VALUE=DATE-TIME:20240304T071244Z
UID:indico-contribution-201-1444@conference2.aau.at
DESCRIPTION:Speakers: Soumen Senapati (RICAM\, Austrian Academy of Science
s)\nDealing with the inverse source problem for the scalar wave equation\,
we have shown recently that we can reconstruct the spacetime dependent so
urce function from the measurement of the wave\, collected on a single poi
nt $x$ and a large enough interval of time\, generated by a small scaled b
ubble\, enjoying large contrasts of its bulk modulus\, injected inside the
domain to image. Here\, we extend this result to reconstruct not only the
source function but also the variable wave speed. Indeed\, from the measu
red waves\, we first localize the internal values of the travel time funct
ion by looking at the behavior of this collected wave in terms of time. Th
en from the Eikonal equation\, we recover the wave speed. Second\, we reco
ver the internal values of the wave generated only by the background (in t
he absence of the small particles) from the same measured data by invertin
g a Volterra integral operator of the second kind. From this reconstructed
wave\, we recover the source function at the expense of a numerical diff
erentiation.\n\nhttps://conference2.aau.at/event/201/contributions/1444/
LOCATION:University of Klagenfurt HS 3
URL:https://conference2.aau.at/event/201/contributions/1444/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Multipoint formulas in inverse problems and their numerical implem
entation
DTSTART;VALUE=DATE-TIME:20230707T090000Z
DTEND;VALUE=DATE-TIME:20230707T092500Z
DTSTAMP;VALUE=DATE-TIME:20240304T071244Z
UID:indico-contribution-201-1443@conference2.aau.at
DESCRIPTION:Speakers: Vladimir Sivkin ()\nWe present the first numerical s
tudy of multipoint formulas for finding leading coefficients in asymptoti
c expansions arising in potential and scattering theories. In particular\,
we implement different formulas for finding the Fourier transform of pot
ential from the scattering amplitude at several high energies. We show tha
t the aforementioned approach can be used for essential numerical improvem
ents of classical results including the slowly convergent Born-Faddeev for
mula for inverse scattering at high energies. The approach of multipoint
formulas can be also used for recovering the X-ray transform of potential
from boundary values of the scattering wave functions at several high ene
rgies. Determination of total charge (electric or gravitational) from seve
ral exterior measurements is also considered. In addition\, we show that t
he aforementioned multipoint formulas admit an efficient regularization fo
r the case of random noise.\n\nhttps://conference2.aau.at/event/201/contri
butions/1443/
LOCATION:University of Klagenfurt HS 2
URL:https://conference2.aau.at/event/201/contributions/1443/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gradient descent-based algorithms for inverse problems in variable
exponent Lebesgue spaces
DTSTART;VALUE=DATE-TIME:20230705T092000Z
DTEND;VALUE=DATE-TIME:20230705T094500Z
DTSTAMP;VALUE=DATE-TIME:20240304T071244Z
UID:indico-contribution-201-1442@conference2.aau.at
DESCRIPTION:Speakers: Marta Lazzaretti (University of Genoa & University o
f Cote d'Azur)\nVariable exponent Lebesgue spaces $\\ell^{(p_n)}$ have bee
n recently proved to be the appropriate functional framework to enforce pi
xel-adaptive regularisation in signal and image processing applications\,
combined with gradient descent (GD) or proximal GD strategies. Compared to
standard Hilbert or Euclidean settings\, however\, the application of the
se algorithms in the Banach setting of $\\ell^{(p_n)}$ is not straightforw
ard due to the lack of a closed-form expression and the non-separability p
roperty of the underlying norm. We propose the use of the associated sepa
rable modular function\, instead of the norm\, to define algorithms based
on GD in $\\ell^{(p_n)}$ and consider a stochastic GD to reduce the per-it
eration cost of iterative schemes\, used to solve linear inverse real-worl
d image reconstruction problems.\n\nhttps://conference2.aau.at/event/201/c
ontributions/1442/
LOCATION:University of Klagenfurt HS 3
URL:https://conference2.aau.at/event/201/contributions/1442/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ultrasound Aberration Correction for Layered Media
DTSTART;VALUE=DATE-TIME:20230706T093500Z
DTEND;VALUE=DATE-TIME:20230706T100000Z
DTSTAMP;VALUE=DATE-TIME:20240304T071244Z
UID:indico-contribution-201-1441@conference2.aau.at
DESCRIPTION:Speakers: Simon Hackl (JKU)\nUltrasound diagnostics is an impo
rtatant\, non-invasive examination method in modern medicine and the recon
struction of an observed object using its reflected ultrasound waves is an
inverse problem of current scientific interest. With focused ultrasound w
aves\, one can look deep inside the human body without causing harm. Howev
er\, a crucial assumption in the theory of focused ultrasound imaging is t
hat the sound speed in the observed medium is constant\, which is not the
case in most clinical applications. It is possible to incorporate differen
t sound speeds into the model\, but at the cost of significantly higher al
gorithmical and computational complexity\, which makes them not applicable
in clinical practice. In this talk\, we present a mathematical framework
for modelling the aberrations caused by a layered medium. Subsequently\, b
y assuming the geometry of the observed object and the sound speed of its
layers to be known\, an aberration correction algorithm is discussed. In t
he usual setting of ultrasound tomography\, these parameters are of course
unknown and have to be calculated from the observed ultrasound data. But
by analyzing the stability of this direct model\, we can determine the nec
essary accuracy in an estimate for the unknown parameters and the resultin
g errors in the inverse problem of reconstruction. The effectiveness of th
e proposed method is shown through numerical simulation using the k-Wave t
oolbox for Matlab. This work is a collaboration with S. Hubmer (RICAM) and
R. Ramlau (JKU).\n\nhttps://conference2.aau.at/event/201/contributions/14
41/
LOCATION:University of Klagenfurt HS 3
URL:https://conference2.aau.at/event/201/contributions/1441/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wave phenomena governed by fractional Moore-Gibson-Thompson equati
ons
DTSTART;VALUE=DATE-TIME:20230706T121000Z
DTEND;VALUE=DATE-TIME:20230706T123500Z
DTSTAMP;VALUE=DATE-TIME:20240304T071244Z
UID:indico-contribution-201-1439@conference2.aau.at
DESCRIPTION:Speakers: Mostafa Meliani (Radboud University)\nIn acoustics\,
higher-order-in-time equations arise when taking into account a class of
(fractional) thermal relaxation laws in the modeling of sound wave propaga
tion. In this talk\, we will discuss the analysis of initial boundary valu
e problems for a family of such equations and determine the behavior of so
lutions as the relaxation time vanishes. The studied model can be viewed a
s a generalization of the well-established (fractional) Moore--Gibson--Tho
mpson equation with three\, in general nonlocal\, convolution terms involv
ing two different kernels. The interplay of these convolutions will influe
nce the uniform analysis and the limiting procedure.\n\nhttps://conference
2.aau.at/event/201/contributions/1439/
LOCATION:University of Klagenfurt HS 3
URL:https://conference2.aau.at/event/201/contributions/1439/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stability estimates for a random inverse source problem
DTSTART;VALUE=DATE-TIME:20230705T141000Z
DTEND;VALUE=DATE-TIME:20230705T143500Z
DTSTAMP;VALUE=DATE-TIME:20240304T071244Z
UID:indico-contribution-201-1438@conference2.aau.at
DESCRIPTION:Speakers: Philipp Mickan ()\nWe consider the inverse random so
urce problem to determine the strength of a random acoustic sound source b
y correlation data generated from the observation of the pressure signal o
f the emitted time harmonic acoustic waves. This model can be applied to a
eroacoustics where regularisation methods for the inverse source problem c
onstitute the best approach to determine a sound source. After uniqueness
has been recently proven for this problem\, we now investigate the stabili
ty properties. This presentation hence contains as one of the main result
a rigorous proof of a logarithmic stability estimate as well as logarithmi
c convergence rates for spectral regularisation methods applied to the inv
erse source problem. These two results are obtained by verifying a variati
onal source condition by methods developed by Hohage and Weidling. Therefo
re\, we establish stability estimates using geometrical optics solutions.
In this talk we will present numerical experiments as well which suggest l
ogarithmic convergence rates.\n\nhttps://conference2.aau.at/event/201/cont
ributions/1438/
LOCATION:University of Klagenfurt HS 3
URL:https://conference2.aau.at/event/201/contributions/1438/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Early stopping of untrained neural networks
DTSTART;VALUE=DATE-TIME:20230705T094500Z
DTEND;VALUE=DATE-TIME:20230705T101000Z
DTSTAMP;VALUE=DATE-TIME:20240304T071244Z
UID:indico-contribution-201-1437@conference2.aau.at
DESCRIPTION:Speakers: Tim Jahn (Universitaet Bonn)\nin recent years new re
gularisation methods based on neural networks have shown promising perform
ance for the solution of ill-posed problems\, e.g.\, in imaging science. D
ue to the non-linearity of the networks\, these methods often lack profoun
d theoretical justification. In this talk we rigorously discuss convergenc
e for an untrained convolutional network. Untrained networks are particula
ry attractive for applications\, since they do not require any training da
ta. Its regularising property is solely based on the architecture of the n
etwork. Because of this\, appropriate early stopping is essential for the
success of the method. We show that the discrepancy principle is an adequa
te method for early stopping here\, as it yields minimax optimal convergen
ce rates.\n\nhttps://conference2.aau.at/event/201/contributions/1437/
LOCATION:University of Klagenfurt HS 3
URL:https://conference2.aau.at/event/201/contributions/1437/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pulse Wave Analysis in the Human Brain
DTSTART;VALUE=DATE-TIME:20230706T114500Z
DTEND;VALUE=DATE-TIME:20230706T121000Z
DTSTAMP;VALUE=DATE-TIME:20240304T071244Z
UID:indico-contribution-201-1435@conference2.aau.at
DESCRIPTION:Speakers: Lukas Weissinger (RICAM/JKU Linz)\nCardiac pulsation
s in the human brain have recentlly garnered interest due to their potenti
al involvement in the pathogenesis of neurodegenerative diseases. The (pul
se) wave\, which describes the velocity of blood flow along an intracrania
l artery\, consists of a forward (anterograde) and backward (retrograde\,
reflected) part\, but the measurement usually consists of a superposition
of these components. In this talk\, we provide a mathematical framework fo
r the inverse problem of estimating the pulse wave velocity as well as the
forward and backward component of the pulse wave separately\, using MRI m
easurements on the middle cerebral artery. Additionally\, we provide an an
alysis of the problem\, which is necessary for the application of a soluti
on method based on an alternate direction approach. The proposed method's
applicability is demonstrated through numerical experiments using simulati
on data.\n\nhttps://conference2.aau.at/event/201/contributions/1435/
LOCATION:University of Klagenfurt HS 3
URL:https://conference2.aau.at/event/201/contributions/1435/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Accelerating the Landweber method for the eikonal equation by a CN
N
DTSTART;VALUE=DATE-TIME:20230705T133500Z
DTEND;VALUE=DATE-TIME:20230705T140000Z
DTSTAMP;VALUE=DATE-TIME:20240304T071244Z
UID:indico-contribution-201-1433@conference2.aau.at
DESCRIPTION:Speakers: Clemens Meiser (Saarlands University)\nThe nonlinear
eikonal equation results as a high frequency approximation of the Helmhol
tz equation\, more generally\, of the wave equation. We investigate the ei
konal equation with respect to the theory of inverse problems in the conte
xt of terahertz tomography. We integrate neural networks in the Landweber
iteration for the reconstruction of the refractive index $n(x)$\, $x\\in\\
Omega$\, of an object. To reduce the computing time in the reconstruction
process\, we substitute the forward operator $F$ by a Convolutional Neural
Network $\\varphi_\\Theta$\, so that we obtain the Landweber step $n_{i+1
}^\\delta = n_i^\\delta - \\omega F'(n_i^\\delta)^*(\\varphi_\\Theta(n_i^\
\delta)-y^\\delta)$. In a second step\, we save energy in the learning pro
cess of our network by generating a sparse forward operator. We add to the
cost functional of the CNN a $l1$-regularization term $\\alpha R(\\Theta)
= \\alpha\\sum_{i=1}^L||\\Theta^{(i)}||_1$\, where $\\alpha$ denotes a re
gularization parameter\, $L$ the amount of layers and $\\Theta^{(i)}$ the
matrix of weights for the associated layer. We compare the normal Landwebe
r method with the learned and sparse one. Numerical results will be presen
ted.\n\nhttps://conference2.aau.at/event/201/contributions/1433/
LOCATION:University of Klagenfurt HS 3
URL:https://conference2.aau.at/event/201/contributions/1433/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Deautoconvolution in the two-dimensional case
DTSTART;VALUE=DATE-TIME:20230705T082000Z
DTEND;VALUE=DATE-TIME:20230705T084500Z
DTSTAMP;VALUE=DATE-TIME:20240304T071244Z
UID:indico-contribution-201-1430@conference2.aau.at
DESCRIPTION:Speakers: Yu Deng (TU Chemnitz)\nWe will have a discussion on
the reconstruction of a real function of two real variables over the unit
square from observations of its autoconvolution on $[0\,2]^2\\subset \\mat
hbb{R}^2$ (full data case) or on $[0\,1]^2$ (limited data case). In an $L^
2$-setting\, twofoldness and uniqueness assertions can be obtained for the
deautoconvolution problem in 2D. Moreover\, by means of an example\, we
will illustrate the ill-posedness and also the stable approximate solution
s to the two-dimensional deautoconvolution problem obtained by Tikhonov-ty
pe regularization with different penalties.\n\nhttps://conference2.aau.at/
event/201/contributions/1430/
LOCATION:University of Klagenfurt HS 3
URL:https://conference2.aau.at/event/201/contributions/1430/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Far field operator splitting and completion for inhomogeneous medi
um scattering
DTSTART;VALUE=DATE-TIME:20230707T081000Z
DTEND;VALUE=DATE-TIME:20230707T083500Z
DTSTAMP;VALUE=DATE-TIME:20240304T071244Z
UID:indico-contribution-201-1429@conference2.aau.at
DESCRIPTION:Speakers: Lisa Schätzle (Karlsruhe Institute of Technology)\n
We consider scattering of time-harmonic acoustic waves by an ensemble of c
ompactly supported penetrable scattering objects in 2D.\nThese scattering
objects are illuminated by an incident plane wave.\nThe resulting total wa
ve is the superposition of incident and scattered wave and solves a scatte
ring problem for the Helmholtz equation.\nFor guaranteeing uniqueness\, th
e scattered wave must fulfill the Sommerfeld radiation condition at infini
ty.\n\nIn our consideration\, measurements of the total wave are replaced
by the corresponding far field operator.\nThis operator contains all infor
mation about the scattered wave far away from the scattering objects for a
ll possible illumination directions.\n\nWe are interested in two inverse p
roblems.\nOn the one hand\, given a limited observation of this far field
operator\, we want to determine its missing part\, which we refer to as op
erator completion problem.\n`Limited observation' in this context means\,
that we do not have access to measurements for all illumination directions
or that we cannot measure in all observation directions around the scatte
ring objects.\nOn the other hand\, given the far field operator for the en
semble of scattering objects\, we want to determine the far field operator
s of the individual scattering objects.\nThis is what we refer to as opera
tor splitting problem.\nMultiple reflection effects cause\, in contrast to
the first problem\, the nonlinearity of this second problem.\n\nWe charac
terize spaces containing the individual\, for the two problems relevant co
mponents of the far field operator.\nOperators in these spaces turn out to
have a low rank and sparsity properties with respect to some known modula
ted Fourier frame.\nFurthermore\, this rank and frame can be determined un
der knowledge of the locations and sizes of the scatterer's components.\n\
nIn my talk I will suggest two reformulations of the inverse problems\, a
least squares norm formulation and a $l^1\\times l^1$-norm minimization\,
and appropriate algorithms for solving these formulations numerically.\nMo
reover\, I will present stability results for these reconstructions and su
pport them by numerical experiments.\n\nhttps://conference2.aau.at/event/2
01/contributions/1429/
LOCATION:University of Klagenfurt HS 2
URL:https://conference2.aau.at/event/201/contributions/1429/
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