2,588 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
Fast tomographic inspection of cylindrical objects
This paper presents a method for improved analysis of objects with an axial
symmetry using X-ray Computed Tomography (CT). Cylindrical coordinates about an
axis fixed to the object form the most natural base to check certain
characteristics of objects that contain such symmetry, as often occurs with
industrial parts. The sampling grid corresponds with the object, allowing for
down-sampling hence reducing the reconstruction time. This is necessary for
in-line applications and fast quality inspection. With algebraic reconstruction
it permits the use of a pre-computed initial volume perfectly suited to fit a
series of scans where same-type objects can have different positions and
orientations, as often encountered in an industrial setting. Weighted
back-projection can also be included when some regions are more likely subject
to change, to improve stability. Building on a Cartesian grid reconstruction
code, the feasibility of reusing the existing ray-tracers is checked against
other researches in the same field.Comment: 13 pages, 13 figures. submitted to Journal Of Nondestructive
Evaluation (https://www.springer.com/journal/10921
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
Recent advances in x-ray cone-beam computed laminography
X-ray computed tomography is a well established volume imaging technique used routinely in medical diagnosis, industrial non-destructive testing, and a wide range of scientific fields. Traditionally, computed tomography uses scanning geometries with a single axis of rotation together with reconstruction algorithms specifically designed for this setup. Recently there has however been increasing interest in more complex scanning geometries. These include so called X-ray computed laminography systems capable of imaging specimens with large lateral dimensions, or large aspect ratios, neither of which are well suited to conventional CT scanning procedures. Developments throughout this field have thus been rapid, including the introduction of novel system trajectories, the application and refinement of various reconstruction methods, and the use of recently developed computational hardware and software techniques to accelerate reconstruction times. Here we examine the advances made in the last several years and consider their impact on the state of the art
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