59,578 research outputs found
A Hybrid Segmentation and D-bar Method for Electrical Impedance Tomography
The Regularized D-bar method for Electrical Impedance Tomography provides a
rigorous mathematical approach for solving the full nonlinear inverse problem
directly, i.e. without iterations. It is based on a low-pass filtering in the
(nonlinear) frequency domain. However, the resulting D-bar reconstructions are
inherently smoothed leading to a loss of edge distinction. In this paper, a
novel approach that combines the rigor of the D-bar approach with the
edge-preserving nature of Total Variation regularization is presented. The
method also includes a data-driven contrast adjustment technique guided by the
key functions (CGO solutions) of the D-bar method. The new TV-Enhanced D-bar
Method produces reconstructions with sharper edges and improved contrast while
still solving the full nonlinear problem. This is achieved by using the
TV-induced edges to increase the truncation radius of the scattering data in
the nonlinear frequency domain thereby increasing the radius of the low pass
filter. The algorithm is tested on numerically simulated noisy EIT data and
demonstrates significant improvements in edge preservation and contrast which
can be highly valuable for absolute EIT imaging
A Data-Driven Edge-Preserving D-bar Method for Electrical Impedance Tomography
In Electrical Impedance Tomography (EIT), the internal conductivity of a body
is recovered via current and voltage measurements taken at its surface. The
reconstruction task is a highly ill-posed nonlinear inverse problem, which is
very sensitive to noise, and requires the use of regularized solution methods,
of which D-bar is the only proven method. The resulting EIT images have low
spatial resolution due to smoothing caused by low-pass filtered regularization.
In many applications, such as medical imaging, it is known \emph{a priori} that
the target contains sharp features such as organ boundaries, as well as
approximate ranges for realistic conductivity values. In this paper, we use
this information in a new edge-preserving EIT algorithm, based on the original
D-bar method coupled with a deblurring flow stopped at a minimal data
discrepancy. The method makes heavy use of a novel data fidelity term based on
the so-called {\em CGO sinogram}. This nonlinear data step provides superior
robustness over traditional EIT data formats such as current-to-voltage
matrices or Dirichlet-to-Neumann operators, for commonly used current patterns.Comment: 24 pages, 11 figure
Enhancement of shock-capturing methods via machine learning
In recent years, machine learning has been used to create data-driven solutions to problems for which an algorithmic solution is intractable, as well as fine-tuning existing algorithms. This research applies machine learning to the development of an improved finite-volume method for simulating PDEs with discontinuous solutions. Shock-capturing methods make use of nonlinear switching functions that are not guaranteed to be optimal. Because data can be used to learn nonlinear relationships, we train a neural network to improve the results of a fifth-order WENO method. We post-process the outputs of the neural network to guarantee that the method is consistent. The training data consist of the exact mapping between cell averages and interpolated values for a set of integrable functions that represent waveforms we would expect to see while simulating a PDE. We demonstrate our method on linear advection of a discontinuous function, the inviscid Burgersâ equation, and the 1-D Euler equations. For the latter, we examine the ShuâOsher model problem for turbulenceâshock wave interactions. We find that our method outperforms WENO in simulations where the numerical solution becomes overly diffused due to numerical viscosity
Inexact Bregman iteration with an application to Poisson data reconstruction
This work deals with the solution of image restoration problems by an
iterative regularization method based on the Bregman iteration. Any iteration of this
scheme requires to exactly compute the minimizer of a function. However, in some
image reconstruction applications, it is either impossible or extremely expensive to
obtain exact solutions of these subproblems. In this paper, we propose an inexact
version of the iterative procedure, where the inexactness in the inner subproblem
solution is controlled by a criterion that preserves the convergence of the Bregman
iteration and its features in image restoration problems. In particular, the method
allows to obtain accurate reconstructions also when only an overestimation of the
regularization parameter is known. The introduction of the inexactness in the iterative
scheme allows to address image reconstruction problems from data corrupted by
Poisson noise, exploiting the recent advances about specialized algorithms for the
numerical minimization of the generalized KullbackâLeibler divergence combined with
a regularization term. The results of several numerical experiments enable to evaluat
Exploring the physical limits of saturation contrast in Magnetic Resonance Imagign
Magnetic Resonance Imaging has become nowadays an indispensable tool with
applications ranging from medicine to material science. However, so far the
physical limits of the maximum achievable experimental contrast were unknown.
We introduce an approach based on principles of optimal control theory to
explore these physical limits, providing a benchmark for numerically optimized
robust pulse sequences which can take into account experimental imperfections.
This approach is demonstrated experimentally using a model system of two
spatially separated liquids corresponding to blood in its oxygenated and
deoxygenated forms.Comment: 11 pages, 4 figures. This paper is in open access, Nature-Scientific
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