2,964 research outputs found
Sparsity prior for electrical impedance tomography with partial data
This paper focuses on prior information for improved sparsity reconstruction
in electrical impedance tomography with partial data, i.e. data measured only
on subsets of the boundary. Sparsity is enforced using an norm of the
basis coefficients as the penalty term in a Tikhonov functional, and prior
information is incorporated by applying a spatially distributed regularization
parameter. The resulting optimization problem allows great flexibility with
respect to the choice of measurement boundaries and incorporation of prior
knowledge. The problem is solved using a generalized conditional gradient
method applying soft thresholding. Numerical examples show that the addition of
prior information in the proposed algorithm gives vastly improved
reconstructions even for the partial data problem. The method is in addition
compared to a total variation approach.Comment: 17 pages, 12 figure
Determining nonsmooth first order terms from partial boundary measurements
We extend results of Dos Santos Ferreira-Kenig-Sjoestrand-Uhlmann
(math.AP/0601466) to less smooth coefficients, and we show that measurements on
part of the boundary for the magnetic Schroedinger operator determine uniquely
the magnetic field related to a Hoelder continuous potential. We give a similar
result for determining a convection term. The proofs involve Carleman
estimates, a smoothing procedure, and an extension of the Nakamura-Uhlmann
pseudodifferential conjugation method to logarithmic Carleman weights
Distinguishability revisited: depth dependent bounds on reconstruction quality in electrical impedance tomography
The reconstruction problem in electrical impedance tomography is highly
ill-posed, and it is often observed numerically that reconstructions have poor
resolution far away from the measurement boundary but better resolution near
the measurement boundary. The observation can be quantified by the concept of
distinguishability of inclusions. This paper provides mathematically rigorous
results supporting the intuition. Indeed, for a model problem lower and upper
bounds on the distinguishability of an inclusion are derived in terms of the
boundary data. These bounds depend explicitly on the distance of the inclusion
to the boundary, i.e. the depth of the inclusion. The results are obtained for
disk inclusions in a homogeneous background in the unit disk. The theoretical
bounds are verified numerically using a novel, exact characterization of the
forward map as a tridiagonal matrix.Comment: 25 pages, 6 figure
Reconstruction of less regular conductivities in the plane
We study the inverse conductivity problem of how to reconstruct an isotropic
electrical conductivity distribution in an object from static
electrical measurements on the boundary of the object. We give an exact
reconstruction algorithm for the conductivity \gamma\in C^{1+\epsilon}(\ol
\Om) in the plane domain from the associated Dirichlet to Neumann map
on \partial \Om. Hence we improve earlier reconstruction results. The method
used relies on a well-known reduction to a first order system, for which the
\ol\partial-method of inverse scattering theory can be applied
Limited Angle Acousto-Electrical Tomography
This paper considers the reconstruction problem in Acousto-Electrical
Tomography, i.e., the problem of estimating a spatially varying conductivity in
a bounded domain from measurements of the internal power densities resulting
from different prescribed boundary conditions. Particular emphasis is placed on
the limited angle scenario, in which the boundary conditions are supported only
on a part of the boundary. The reconstruction problem is formulated as an
optimization problem in a Hilbert space setting and solved using Landweber
iteration. The resulting algorithm is implemented numerically in two spatial
dimensions and tested on simulated data. The results quantify the intuition
that features close to the measurement boundary are stably reconstructed and
features further away are less well reconstructed. Finally, the ill-posedness
of the limited angle problem is quantified numerically using the singular value
decomposition of the corresponding linearized problem.Comment: 23 page
Simulation of waviness in neutron guides
As the trend of neutron guide designs points towards longer and more complex
guides, imperfections such as waviness becomes increasingly important.
Simulations of guide waviness has so far been limited by a lack of reasonable
waviness models. We here present a stochastic description of waviness and its
implementation in the McStas simulation package. The effect of this new
implementation is compared to the guide simulations without waviness and the
simple, yet unphysical, waviness model implemented in McStas 1.12c and 2.0
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