1,723 research outputs found
Gaussian process tomography for soft x-ray spectroscopy at WEST without equilibrium information
International audienceGaussian process tomography (GPT) is a recently developed tomography method based on the Bayesian probability theory [J. Svensson, JET Internal Report EFDA-JET-PR(11)24, 2011 and Li et al., Rev. Sci. Instrum. 84, 083506 (2013)]. By modeling the soft X-ray (SXR) emissivity field in a poloidal cross section as a Gaussian process, the Bayesian SXR tomography can be carried out in a robust and extremely fast way. Owing to the short execution time of the algorithm, GPT is an important candidate for providing real-time reconstructions with a view to impurity transport and fast magnetohydrodynamic control. In addition, the Bayesian formalism allows quantifying uncertainty on the inferred parameters. In this paper, the GPT technique is validated using a synthetic data set expected from the WEST tokamak, and the results are shown of its application to the reconstruction of SXR emissivity profiles measured on Tore Supra. The method is compared with the standard algorithm based on minimization of the Fisher information
Time-Dependent Tomographic Reconstruction of the Solar Corona
Solar rotational tomography (SRT) applied to white-light coronal images
observed at multiple aspect angles has been the preferred approach for
determining the three-dimensional (3D) electron density structure of the solar
corona. However, it is seriously hampered by the restrictive assumption that
the corona is time-invariant which introduces significant errors in the
reconstruction. We first explore several methods to mitigate the temporal
variation of the corona by decoupling the "fast-varying" inner corona from the
"slow-moving" outer corona using multiple masking (either by juxtaposition or
recursive combination) and radial weighting. Weighting with a radial
exponential profile provides some improvement over a classical reconstruction
but only beyond 3 Rsun. We next consider a full time-dependent tomographic
reconstruction involving spatio-temporal regularization and further introduce a
co-rotating regularization aimed at preventing concentration of reconstructed
density in the plane of the sky. Crucial to testing our procedure and properly
tuning the regularization parameters is the introduction of a time-dependent
MHD model of the corona based on observed magnetograms to build a time-series
of synthetic images of the corona. Our procedure, which successfully reproduces
the time-varying model corona, is finally applied to a set of of 53 LASCO-C2 pB
images roughly evenly spaced in time from 15 to 29 March 2009. Our procedure
paves the way to a time-dependent tomographic reconstruction of the coronal
electron density to the whole set of LASCO-C2 images presently spanning 20
years.Comment: 24 pages, 18 figure
Regularized Newton Methods for X-ray Phase Contrast and General Imaging Problems
Like many other advanced imaging methods, x-ray phase contrast imaging and
tomography require mathematical inversion of the observed data to obtain
real-space information. While an accurate forward model describing the
generally nonlinear image formation from a given object to the observations is
often available, explicit inversion formulas are typically not known. Moreover,
the measured data might be insufficient for stable image reconstruction, in
which case it has to be complemented by suitable a priori information. In this
work, regularized Newton methods are presented as a general framework for the
solution of such ill-posed nonlinear imaging problems. For a proof of
principle, the approach is applied to x-ray phase contrast imaging in the
near-field propagation regime. Simultaneous recovery of the phase- and
amplitude from a single near-field diffraction pattern without homogeneity
constraints is demonstrated for the first time. The presented methods further
permit all-at-once phase contrast tomography, i.e. simultaneous phase retrieval
and tomographic inversion. We demonstrate the potential of this approach by
three-dimensional imaging of a colloidal crystal at 95 nm isotropic resolution.Comment: (C)2016 Optical Society of America. One print or electronic copy may
be made for personal use only. Systematic reproduction and distribution,
duplication of any material in this paper for a fee or for commercial
purposes, or modifications of the content of this paper are prohibite
3D electron density distributions in the solar corona during solar minima: assessment for more realistic solar wind modeling
Knowledge of the electron density distribution in the solar corona put
constraints on the magnetic field configurations for coronal modeling and on
initial conditions for solar wind modeling. We work with polarized
SOHO/LASCO-C2 images from the last two recent minima of solar activity
(1996-1997 and 2008-2010), devoid of coronal mass ejections. The goals are to
derive the 4D electron density distributions in the corona by applying a newly
developed time-dependent tomographic reconstruction method and to compare the
results between the two solar minima and with two magnetohydrodynamic models.
First, we confirm that the values of the density distribution in thermodynamic
models are more realistic than in polytropic ones. The tomography provides more
accurate distributions in the polar regions, and we find that the density in
tomographic and thermodynamic solutions varies with the solar cycle in both
polar and equatorial regions. Second, we find that the highest-density
structures do not always correspond to the predicted large-scale heliospheric
current sheet or its helmet streamer but can follow the locations of
pseudo-streamers. We deduce that tomography offers reliable density
distributions in the corona, reproducing the slow time evolution of coronal
structures, without prior knowledge of the coronal magnetic field over a full
rotation. Finally, we suggest that the highest-density structures show a
differential rotation well above the surface depending on how they are
magnetically connected to the surface. Such valuable information on the
rotation of large-scale structures could help to connect the sources of the
solar wind to their in situ counterparts in future missions such as Solar
Orbiter and Solar Probe Plus.Comment: 23 pages, 9 figure
Quick X-ray microtomography using a laser-driven betatron source
Laser-driven X-ray sources are an emerging alternative to conventional X-ray
tubes and synchrotron sources. We present results on microtomographic X-ray
imaging of a cancellous human bone sample using synchrotron-like betatron
radiation. The source is driven by a 100-TW-class titanium-sapphire laser
system and delivers over X-ray photons per second. Compared to earlier
studies, the acquisition time for an entire tomographic dataset has been
reduced by more than an order of magnitude. Additionally, the reconstruction
quality benefits from the use of statistical iterative reconstruction
techniques. Depending on the desired resolution, tomographies are thereby
acquired within minutes, which is an important milestone towards real-life
applications of laser-plasma X-ray sources
Solving ill-posed inverse problems using iterative deep neural networks
We propose a partially learned approach for the solution of ill posed inverse
problems with not necessarily linear forward operators. The method builds on
ideas from classical regularization theory and recent advances in deep learning
to perform learning while making use of prior information about the inverse
problem encoded in the forward operator, noise model and a regularizing
functional. The method results in a gradient-like iterative scheme, where the
"gradient" component is learned using a convolutional network that includes the
gradients of the data discrepancy and regularizer as input in each iteration.
We present results of such a partially learned gradient scheme on a non-linear
tomographic inversion problem with simulated data from both the Sheep-Logan
phantom as well as a head CT. The outcome is compared against FBP and TV
reconstruction and the proposed method provides a 5.4 dB PSNR improvement over
the TV reconstruction while being significantly faster, giving reconstructions
of 512 x 512 volumes in about 0.4 seconds using a single GPU
A parametric level-set method for partially discrete tomography
This paper introduces a parametric level-set method for tomographic
reconstruction of partially discrete images. Such images consist of a
continuously varying background and an anomaly with a constant (known)
grey-value. We represent the geometry of the anomaly using a level-set
function, which we represent using radial basis functions. We pose the
reconstruction problem as a bi-level optimization problem in terms of the
background and coefficients for the level-set function. To constrain the
background reconstruction we impose smoothness through Tikhonov regularization.
The bi-level optimization problem is solved in an alternating fashion; in each
iteration we first reconstruct the background and consequently update the
level-set function. We test our method on numerical phantoms and show that we
can successfully reconstruct the geometry of the anomaly, even from limited
data. On these phantoms, our method outperforms Total Variation reconstruction,
DART and P-DART.Comment: Paper submitted to 20th International Conference on Discrete Geometry
for Computer Imager
GENFIRE: A generalized Fourier iterative reconstruction algorithm for high-resolution 3D imaging
Tomography has made a radical impact on diverse fields ranging from the study
of 3D atomic arrangements in matter to the study of human health in medicine.
Despite its very diverse applications, the core of tomography remains the same,
that is, a mathematical method must be implemented to reconstruct the 3D
structure of an object from a number of 2D projections. In many scientific
applications, however, the number of projections that can be measured is
limited due to geometric constraints, tolerable radiation dose and/or
acquisition speed. Thus it becomes an important problem to obtain the
best-possible reconstruction from a limited number of projections. Here, we
present the mathematical implementation of a tomographic algorithm, termed
GENeralized Fourier Iterative REconstruction (GENFIRE). By iterating between
real and reciprocal space, GENFIRE searches for a global solution that is
concurrently consistent with the measured data and general physical
constraints. The algorithm requires minimal human intervention and also
incorporates angular refinement to reduce the tilt angle error. We demonstrate
that GENFIRE can produce superior results relative to several other popular
tomographic reconstruction techniques by numerical simulations, and by
experimentally by reconstructing the 3D structure of a porous material and a
frozen-hydrated marine cyanobacterium. Equipped with a graphical user
interface, GENFIRE is freely available from our website and is expected to find
broad applications across different disciplines.Comment: 18 pages, 6 figure
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