982 research outputs found
Automatic alignment for three-dimensional tomographic reconstruction
In tomographic reconstruction, the goal is to reconstruct an unknown object
from a collection of line integrals. Given a complete sampling of such line
integrals for various angles and directions, explicit inverse formulas exist to
reconstruct the object. Given noisy and incomplete measurements, the inverse
problem is typically solved through a regularized least-squares approach. A
challenge for both approaches is that in practice the exact directions and
offsets of the x-rays are only known approximately due to, e.g. calibration
errors. Such errors lead to artifacts in the reconstructed image. In the case
of sufficient sampling and geometrically simple misalignment, the measurements
can be corrected by exploiting so-called consistency conditions. In other
cases, such conditions may not apply and we have to solve an additional inverse
problem to retrieve the angles and shifts. In this paper we propose a general
algorithmic framework for retrieving these parameters in conjunction with an
algebraic reconstruction technique. The proposed approach is illustrated by
numerical examples for both simulated data and an electron tomography dataset
Nanometer-scale Tomographic Reconstruction of 3D Electrostatic Potentials in GaAs/AlGaAs Core-Shell Nanowires
We report on the development of Electron Holographic Tomography towards a
versatile potential measurement technique, overcoming several limitations, such
as a limited tilt range, previously hampering a reproducible and accurate
electrostatic potential reconstruction in three dimensions. Most notably,
tomographic reconstruction is performed on optimally sampled polar grids taking
into account symmetry and other spatial constraints of the nanostructure.
Furthermore, holographic tilt series acquisition and alignment have been
automated and adapted to three dimensions. We demonstrate 6 nm spatial and 0.2
V signal resolution by reconstructing various, previously hidden, potential
details of a GaAs/AlGaAs core-shell nanowire. The improved tomographic
reconstruction opens pathways towards the detection of minute potentials in
nanostructures and an increase in speed and accuracy in related techniques such
as X-ray tomography
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
Compressed Sensing Based Reconstruction Algorithm for X-ray Dose Reduction in Synchrotron Source Micro Computed Tomography
Synchrotron computed tomography requires a large number of angular projections to reconstruct tomographic images with high resolution for detailed and accurate diagnosis. However, this exposes the specimen to a large amount of x-ray radiation. Furthermore, this increases scan time and, consequently, the likelihood of involuntary specimen movements. One approach for decreasing the total scan time and radiation dose is to reduce the number of projection views needed to reconstruct the images. However, the aliasing artifacts appearing in the image due to the reduced number of projection data, visibly degrade the image quality. According to the compressed sensing theory, a signal can be accurately reconstructed from highly undersampled data by solving an optimization problem, provided that the signal can be sparsely represented in a predefined transform domain. Therefore, this thesis is mainly concerned with designing compressed sensing-based reconstruction algorithms to suppress aliasing artifacts while preserving spatial resolution in the resulting reconstructed image. First, the reduced-view synchrotron computed tomography reconstruction is formulated as a total variation regularized compressed sensing problem. The Douglas-Rachford Splitting and the randomized Kaczmarz methods are utilized to solve the optimization problem of the compressed sensing formulation.
In contrast with the first part, where consistent simulated projection data are generated for image reconstruction, the reduced-view inconsistent real ex-vivo synchrotron absorption contrast micro computed tomography bone data are used in the second part. A gradient regularized compressed sensing problem is formulated, and the Douglas-Rachford Splitting and the preconditioned conjugate gradient methods are utilized to solve the optimization problem of the compressed sensing formulation. The wavelet image denoising algorithm is used as the post-processing algorithm to attenuate the unwanted staircase artifact generated by the reconstruction algorithm.
Finally, a noisy and highly reduced-view inconsistent real in-vivo synchrotron phase-contrast computed tomography bone data are used for image reconstruction. A combination of prior image constrained compressed sensing framework, and the wavelet regularization is formulated, and the Douglas-Rachford Splitting and the preconditioned conjugate gradient methods are utilized to solve the optimization problem of the compressed sensing formulation. The prior image constrained compressed sensing framework takes advantage of the prior image to promote the sparsity of the target image. It may lead to an unwanted staircase artifact when applied to noisy and texture images, so the wavelet regularization is used to attenuate the unwanted staircase artifact generated by the prior image constrained compressed sensing reconstruction algorithm.
The visual and quantitative performance assessments with the reduced-view simulated and real computed tomography data from canine prostate tissue, rat forelimb, and femoral cortical bone samples, show that the proposed algorithms have fewer artifacts and reconstruction errors than other conventional reconstruction algorithms at the same x-ray dose
The Application of Preconditioned Alternating Direction Method of Multipliers in Depth from Focal Stack
Post capture refocusing effect in smartphone cameras is achievable by using
focal stacks. However, the accuracy of this effect is totally dependent on the
combination of the depth layers in the stack. The accuracy of the extended
depth of field effect in this application can be improved significantly by
computing an accurate depth map which has been an open issue for decades. To
tackle this issue, in this paper, a framework is proposed based on
Preconditioned Alternating Direction Method of Multipliers (PADMM) for depth
from the focal stack and synthetic defocus application. In addition to its
ability to provide high structural accuracy and occlusion handling, the
optimization function of the proposed method can, in fact, converge faster and
better than state of the art methods. The evaluation has been done on 21 sets
of focal stacks and the optimization function has been compared against 5 other
methods. Preliminary results indicate that the proposed method has a better
performance in terms of structural accuracy and optimization in comparison to
the current state of the art methods.Comment: 15 pages, 8 figure
Registration-based multi-orientation tomography
We propose a combination of an experimental approach and a reconstruction technique that leads to reduction of artefacts in X-ray computer tomography of strongly attenuating objects. Through fully automatic data alignment, data generated in multiple experiments with varying object orientations are combined. Simulations and exp
- …