2,360 research outputs found
Moment-based angular difference estimation between two tomographic projections in 2D and 3D
International audienceThis paper introduces a new method for estimating the angular difference between two tomographic projections belonging to a set of projections taken at unknown directions in 2D and 3D. Our method relies on the projection neighbor selection in projection moment space, the calculation of the angular differences between these neighboring projections using moment properties and a projection moment neighborhood graph. The accuracy and the robustness of our method are shown on a test database including fifty 2D and 3D gray-level images at different resolutions and with different levels of noise
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
Direct 3D Tomographic Reconstruction and Phase-Retrieval of Far-Field Coherent Diffraction Patterns
We present an alternative numerical reconstruction algorithm for direct
tomographic reconstruction of a sample refractive indices from the measured
intensities of its far-field coherent diffraction patterns. We formulate the
well-known phase-retrieval problem in ptychography in a tomographic framework
which allows for simultaneous reconstruction of the illumination function and
the sample refractive indices in three dimensions. Our iterative reconstruction
algorithm is based on the Levenberg-Marquardt algorithm. We demonstrate the
performance of our proposed method with simulation studies
Geometric reconstruction methods for electron tomography
Electron tomography is becoming an increasingly important tool in materials
science for studying the three-dimensional morphologies and chemical
compositions of nanostructures. The image quality obtained by many current
algorithms is seriously affected by the problems of missing wedge artefacts and
nonlinear projection intensities due to diffraction effects. The former refers
to the fact that data cannot be acquired over the full tilt range;
the latter implies that for some orientations, crystalline structures can show
strong contrast changes. To overcome these problems we introduce and discuss
several algorithms from the mathematical fields of geometric and discrete
tomography. The algorithms incorporate geometric prior knowledge (mainly
convexity and homogeneity), which also in principle considerably reduces the
number of tilt angles required. Results are discussed for the reconstruction of
an InAs nanowire
Ptychographic X-ray computed tomography of extended colloidal networks in food emulsions
As a main structural level in colloidal food materials, extended colloidal
networks are important for texture and rheology. By obtaining the 3D
microstructure of the network, macroscopic mechanical properties of the
material can be inferred. However, this approach is hampered by the lack of
suitable non-destructive 3D imaging techniques with submicron resolution.
We present results of quantitative ptychographic X-ray computed tomography
applied to a palm kernel oil based oil-in-water emulsion. The measurements were
carried out at ambient pressure and temperature. The 3D structure of the
extended colloidal network of fat globules was obtained with a resolution of
around 300 nm. Through image analysis of the network structure, the fat globule
size distribution was computed and compared to previous findings. In further
support, the reconstructed electron density values were within 4% of reference
values.Comment: 19 pages, 4 figures, to be published in Food Structur
Analysis of Tomographic Reconstruction of 2D Images using the Distribution of Unknown Projection Angles
It is well known that a band-limited signal can be reconstructed from its
uniformly spaced samples if the sampling rate is sufficiently high. More
recently, it has been proved that one can reconstruct a 1D band-limited signal
even if the exact sample locations are unknown, but given just the distribution
of the sample locations and their ordering in 1D. In this work, we extend the
analytical bounds on the reconstruction error in such scenarios for
quasi-bandlimited signals. We also prove that the method for such a
reconstruction is resilient to a certain proportion of errors in the
specification of the sample location ordering. We then express the problem of
tomographic reconstruction of 2D images from 1D Radon projections under unknown
angles with known angle distribution, as a special case for reconstruction of
quasi-bandlimited signals from samples at unknown locations with known
distribution. Building upon our theoretical background, we present asymptotic
bounds for 2D quasi-bandlimited image reconstruction from 1D Radon projections
in the unknown angles setting, which commonly occurs in cryo-electron
microscopy (cryo-EM). To the best of our knowledge, this is the first piece of
work to perform such an analysis for 2D cryo-EM, even though the associated
reconstruction algorithms have been known for a long time
Fast algorithms and efficient GPU implementations for the Radon transform and the back-projection operator represented as convolution operators
The Radon transform and its adjoint, the back-projection operator, can both
be expressed as convolutions in log-polar coordinates. Hence, fast algorithms
for the application of the operators can be constructed by using FFT, if data
is resampled at log-polar coordinates. Radon data is typically measured on an
equally spaced grid in polar coordinates, and reconstructions are represented
(as images) in Cartesian coordinates. Therefore, in addition to FFT, several
steps of interpolation have to be conducted in order to apply the Radon
transform and the back-projection operator by means of convolutions.
Both the interpolation and the FFT operations can be efficiently implemented
on Graphical Processor Units (GPUs). For the interpolation, it is possible to
make use of the fact that linear interpolation is hard-wired on GPUs, meaning
that it has the same computational cost as direct memory access. Cubic order
interpolation schemes can be constructed by combining linear interpolation
steps which provides important computation speedup.
We provide details about how the Radon transform and the back-projection can
be implemented efficiently as convolution operators on GPUs. For large data
sizes, speedups of about 10 times are obtained in relation to the computational
times of other software packages based on GPU implementations of the Radon
transform and the back-projection operator. Moreover, speedups of more than a
1000 times are obtained against the CPU-implementations provided in the MATLAB
image processing toolbox
Complete Photoionization Experiments via Ultrafast Coherent Control with Polarization Multiplexing II: Numerics & Analysis Methodologies
The feasibility of complete photoionization experiments, in which the full
set of photoionization matrix elements are determined, using multiphoton
ionization schemes with polarization-shaped pulses has recently been
demonstrated [Hockett et. al., Phys. Rev. Lett. 112, 223001 (2014)]. Here we
extend on our previous work to discuss further details of the numerics and
analysis methodology utilised, and compare the results directly to new
tomographic photoelectron measurements, which provide a more sensitive test of
the validity of the results. In so doing we discuss in detail the physics of
the photoionziation process, and suggest various avenues and prospects for this
coherent multiplexing methodology
- …