9,478 research outputs found
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
Orthogonal Matrix Retrieval in Cryo-Electron Microscopy
In single particle reconstruction (SPR) from cryo-electron microscopy
(cryo-EM), the 3D structure of a molecule needs to be determined from its 2D
projection images taken at unknown viewing directions. Zvi Kam showed already
in 1980 that the autocorrelation function of the 3D molecule over the rotation
group SO(3) can be estimated from 2D projection images whose viewing directions
are uniformly distributed over the sphere. The autocorrelation function
determines the expansion coefficients of the 3D molecule in spherical harmonics
up to an orthogonal matrix of size for each
. In this paper we show how techniques for solving the phase
retrieval problem in X-ray crystallography can be modified for the cryo-EM
setup for retrieving the missing orthogonal matrices. Specifically, we present
two new approaches that we term Orthogonal Extension and Orthogonal
Replacement, in which the main algorithmic components are the singular value
decomposition and semidefinite programming. We demonstrate the utility of these
approaches through numerical experiments on simulated data.Comment: Modified introduction and summary. Accepted to the IEEE International
Symposium on Biomedical Imagin
A hybrid 3-D reconstruction/registration algorithm for correction of head motion in emission tomography
Even with head restraint, small head movements can occur during data acquisition in emission tomography that are sufficiently large to result in detectable artifacts in the final reconstruction. Direct measurement of motion can be cumbersome and difficult to implement, whereas previous attempts to use the measured projection data for correction have been limited to simple translation orthogonal to the projection. A fully three-dimensional (3-D) algorithm is proposed that estimates the patient orientation based on the projection of motion-corrupted data, with incorporation of motion information within subsequent ordered-subset expectation-maximization subiterations. Preliminary studies have been performed using a digital version of the Hoffman brain phantom. Movement was simulated by constructing a mixed set of projections in discrete positions of the phantom. The algorithm determined the phantom orientation that best matched each constructed projection with its corresponding measured projection. In the case of a simulated single movement in 24 of 64 projections, all misaligned projections were correctly identified. Incorporating data at the determined object orientation resulted in a reduction of mean square difference (MSD) between motion-corrected and motion-free reconstructions, compared to the MSD between uncorrected and motion-free reconstructions, by a factor of 1.9
Linear chemically sensitive electron tomography using DualEELS and dictionary-based compressed sensing
We have investigated the use of DualEELS in elementally sensitive tilt series tomography in the scanning transmission electron microscope. A procedure is implemented using deconvolution to remove the effects of multiple scattering, followed by normalisation by the zero loss peak intensity. This is performed to produce a signal that is linearly dependent on the projected density of the element in each pixel. This method is compared with one that does not include deconvolution (although normalisation by the zero loss peak intensity is still performed). Additionaly, we compare the 3D reconstruction using a new compressed sensing algorithm, DLET, with the well-established SIRT algorithm. VC precipitates, which are extracted from a steel on a carbon replica, are used in this study. It is found that the use of this linear signal results in a very even density throughout the precipitates. However, when deconvolution is omitted, a slight density reduction is observed in the cores of the precipitates (a so-called cupping artefact). Additionally, it is clearly demonstrated that the 3D morphology is much better reproduced using the DLET algorithm, with very little elongation in the missing wedge direction. It is therefore concluded that reliable elementally sensitive tilt tomography using EELS requires the appropriate use of DualEELS together with a suitable reconstruction algorithm, such as the compressed sensing based reconstruction algorithm used here, to make the best use of the limited data volume and signal to noise inherent in core-loss EELS
A hybrid 3d reconstruction/registration algorithm for correction of head motion in emission tomography
Even with head restraint, small head movements can occur during data acquisition for emission tomography, sufficiently large to result in detectable artifacts in the final reconstruction. Direct measurement of motion can be cumbersome and difficult to implement, whereas previous attempts to correct for motion based on measured projections have been limited to simple translation orthogonal to the projection. A fully 3D algorithm is proposed that estimates the patient orientation at any time based on the projection of motion-corrupted data, with incorporation of the measured motion within subsequent OSEM sub-iterations. Preliminary studies have been performed using a digital version of the Hoffman brain phantom. Movement was simulated by constructing a mixed set of projections in two discrete positions of the phantom. The algorithm determined the phantom orientation that best aligned each constructed projection with its corresponding, measured projection. In the case of simulated movement of 24 of 64 projections, all mis-positioned projections were correctly identified. The algorithm resulted in a reduction of mean square difference (MSD) between motion corrected and motion-free reconstructions compared to the MSD between uncorrected and motion-free reconstructions by a factor of 2.7
Stable, Robust and Super Fast Reconstruction of Tensors Using Multi-Way Projections
In the framework of multidimensional Compressed Sensing (CS), we introduce an
analytical reconstruction formula that allows one to recover an th-order
data tensor
from a reduced set of multi-way compressive measurements by exploiting its low
multilinear-rank structure. Moreover, we show that, an interesting property of
multi-way measurements allows us to build the reconstruction based on
compressive linear measurements taken only in two selected modes, independently
of the tensor order . In addition, it is proved that, in the matrix case and
in a particular case with rd-order tensors where the same 2D sensor operator
is applied to all mode-3 slices, the proposed reconstruction
is stable in the sense that the approximation
error is comparable to the one provided by the best low-multilinear-rank
approximation, where is a threshold parameter that controls the
approximation error. Through the analysis of the upper bound of the
approximation error we show that, in the 2D case, an optimal value for the
threshold parameter exists, which is confirmed by our
simulation results. On the other hand, our experiments on 3D datasets show that
very good reconstructions are obtained using , which means that this
parameter does not need to be tuned. Our extensive simulation results
demonstrate the stability and robustness of the method when it is applied to
real-world 2D and 3D signals. A comparison with state-of-the-arts sparsity
based CS methods specialized for multidimensional signals is also included. A
very attractive characteristic of the proposed method is that it provides a
direct computation, i.e. it is non-iterative in contrast to all existing
sparsity based CS algorithms, thus providing super fast computations, even for
large datasets.Comment: Submitted to IEEE Transactions on Signal Processin
3D particle tracking velocimetry using dynamic discrete tomography
Particle tracking velocimetry in 3D is becoming an increasingly important
imaging tool in the study of fluid dynamics, combustion as well as plasmas. We
introduce a dynamic discrete tomography algorithm for reconstructing particle
trajectories from projections. The algorithm is efficient for data from two
projection directions and exact in the sense that it finds a solution
consistent with the experimental data. Non-uniqueness of solutions can be
detected and solutions can be tracked individually
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