40,623 research outputs found
Extending holographic LEED to ordered small unit cell superstructures
Following on the success of the recent application of holographic LEED to the
determination of the 3D atomic geometry of Si adatoms on a SiC(111) p(3x3)
surface, which enabled that structure to be solved, we show in this paper that
a similar technique allows the direct recovery of the local geometry of
adsorbates forming superstructures as small as p(2x2), even in the presence of
a local substrate reconstruction.Comment: 10 pages, 5 figures postscript included, revtex, Phys. Rev. B in
pres
Learning-based Single-step Quantitative Susceptibility Mapping Reconstruction Without Brain Extraction
Quantitative susceptibility mapping (QSM) estimates the underlying tissue
magnetic susceptibility from MRI gradient-echo phase signal and typically
requires several processing steps. These steps involve phase unwrapping, brain
volume extraction, background phase removal and solving an ill-posed inverse
problem. The resulting susceptibility map is known to suffer from inaccuracy
near the edges of the brain tissues, in part due to imperfect brain extraction,
edge erosion of the brain tissue and the lack of phase measurement outside the
brain. This inaccuracy has thus hindered the application of QSM for measuring
the susceptibility of tissues near the brain edges, e.g., quantifying cortical
layers and generating superficial venography. To address these challenges, we
propose a learning-based QSM reconstruction method that directly estimates the
magnetic susceptibility from total phase images without the need for brain
extraction and background phase removal, referred to as autoQSM. The neural
network has a modified U-net structure and is trained using QSM maps computed
by a two-step QSM method. 209 healthy subjects with ages ranging from 11 to 82
years were employed for patch-wise network training. The network was validated
on data dissimilar to the training data, e.g. in vivo mouse brain data and
brains with lesions, which suggests that the network has generalized and
learned the underlying mathematical relationship between magnetic field
perturbation and magnetic susceptibility. AutoQSM was able to recover magnetic
susceptibility of anatomical structures near the edges of the brain including
the veins covering the cortical surface, spinal cord and nerve tracts near the
mouse brain boundaries. The advantages of high-quality maps, no need for brain
volume extraction and high reconstruction speed demonstrate its potential for
future applications.Comment: 26 page
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
Optimization Methods for Inverse Problems
Optimization plays an important role in solving many inverse problems.
Indeed, the task of inversion often either involves or is fully cast as a
solution of an optimization problem. In this light, the mere non-linear,
non-convex, and large-scale nature of many of these inversions gives rise to
some very challenging optimization problems. The inverse problem community has
long been developing various techniques for solving such optimization tasks.
However, other, seemingly disjoint communities, such as that of machine
learning, have developed, almost in parallel, interesting alternative methods
which might have stayed under the radar of the inverse problem community. In
this survey, we aim to change that. In doing so, we first discuss current
state-of-the-art optimization methods widely used in inverse problems. We then
survey recent related advances in addressing similar challenges in problems
faced by the machine learning community, and discuss their potential advantages
for solving inverse problems. By highlighting the similarities among the
optimization challenges faced by the inverse problem and the machine learning
communities, we hope that this survey can serve as a bridge in bringing
together these two communities and encourage cross fertilization of ideas.Comment: 13 page
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