1,748 research outputs found
Boundary length of reconstructions in discrete tomography
We consider possible reconstructions of a binary image of which the row and
column sums are given. For any reconstruction we can define the length of the
boundary of the image. In this paper we prove a new lower bound on the length
of this boundary. In contrast to simple bounds that have been derived
previously, in this new lower bound the information of both row and column sums
is combined
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
Non-convex image reconstruction via Expectation Propagation
Tomographic image reconstruction can be mapped to a problem of finding
solutions to a large system of linear equations which maximize a function that
includes \textit{a priori} knowledge regarding features of typical images such
as smoothness or sharpness. This maximization can be performed with standard
local optimization tools when the function is concave, but it is generally
intractable for realistic priors, which are non-concave. We introduce a new
method to reconstruct images obtained from Radon projections by using
Expectation Propagation, which allows us to reframe the problem from an
Bayesian inference perspective. We show, by means of extensive simulations,
that, compared to state-of-the-art algorithms for this task, Expectation
Propagation paired with very simple but non log-concave priors, is often able
to reconstruct images up to a smaller error while using a lower amount of
information per pixel. We provide estimates for the critical rate of
information per pixel above which recovery is error-free by means of
simulations on ensembles of phantom and real images.Comment: 12 pages, 6 figure
Demonstration of Robust Quantum Gate Tomography via Randomized Benchmarking
Typical quantum gate tomography protocols struggle with a self-consistency
problem: the gate operation cannot be reconstructed without knowledge of the
initial state and final measurement, but such knowledge cannot be obtained
without well-characterized gates. A recently proposed technique, known as
randomized benchmarking tomography (RBT), sidesteps this self-consistency
problem by designing experiments to be insensitive to preparation and
measurement imperfections. We implement this proposal in a superconducting
qubit system, using a number of experimental improvements including
implementing each of the elements of the Clifford group in single `atomic'
pulses and custom control hardware to enable large overhead protocols. We show
a robust reconstruction of several single-qubit quantum gates, including a
unitary outside the Clifford group. We demonstrate that RBT yields physical
gate reconstructions that are consistent with fidelities obtained by randomized
benchmarking
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
Bounds for discrete tomography solutions
We consider the reconstruction of a function on a finite subset of
if the line sums in certain directions are prescribed. The real
solutions form a linear manifold, its integer solutions a grid. First we
provide an explicit expression for the projection vector from the origin onto
the linear solution manifold in the case of only row and column sums of a
finite subset of . Next we present a method to estimate the
maximal distance between two binary solutions. Subsequently we deduce an upper
bound for the distance from any given real solution to the nearest integer
solution. This enables us to estimate the stability of solutions. Finally we
generalize the first mentioned result to the torus case and to the continuous
case
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
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