146,793 research outputs found
Estimating View Parameters From Random Projections for Tomography Using Spherical MDS
Background
During the past decade, the computed tomography has been successfully applied to various fields especially in medicine. The estimation of view angles for projections is necessary in some special applications of tomography, for example, the structuring of viruses using electron microscopy and the compensation of the patient\u27s motion over long scanning period. Methods
This work introduces a novel approach, based on the spherical multidimensional scaling (sMDS), which transforms the problem of the angle estimation to a sphere constrained embedding problem. The proposed approach views each projection as a high dimensional vector with dimensionality equal to the number of sampling points on the projection. By using SMDS, then each projection vector is embedded onto a 1D sphere which parameterizes the projection with respect to view angles in a globally consistent manner. The parameterized projections are used for the final reconstruction of the image through the inverse radon transform. The entire reconstruction process is non-iterative and computationally efficient. Results
The effectiveness of the sMDS is verified with various experiments, including the evaluation of the reconstruction quality from different number of projections and resistance to different noise levels. The experimental results demonstrate the efficiency of the proposed method. Conclusion
Our study provides an effective technique for the solution of 2D tomography with unknown acquisition view angles. The proposed method will be extended to three dimensional reconstructions in our future work. All materials, including source code and demos, are available onhttps://engineering.purdue.edu/PRECISE/SMDS
Well-posedness for the motion of an incompressible liquid with free surface boundary
We study the motion of an incompressible perfect liquid body in vacuum. This
can be thought of as a model for the motion of the ocean or a star. The free
surface moves with the velocity of the liquid and the pressure vanishes on the
free surface. This leads to a free boundary problem for Euler's equations,
where the regularity of the boundary enters to highest order. We prove local
existence in Sobolev spaces assuming a "physical condition", related to the
fact that the pressure of a fluid has to be positive.Comment: To appear in the Annals of Mat
Schroedinger functional formalism with domain-wall fermion
Finite volume renormalization scheme is one of the most fascinating scheme
for non-perturbative renormalization on lattice.
By using the step scaling function one can follow running of renormalized
quantities with reasonable cost.
It has been established the Schroedinger functional is very convenient to
define a field theory in a finite volume for the renormalization scheme.
The Schroedinger functional, which is characterized by a
Dirichlet boundary condition in temporal direction, is well defined and works
well for the Yang-Mills theory and QCD with the Wilson fermion.
However one easily runs into difficulties if one sets the same sort of the
Dirichlet boundary condition for the overlap Dirac operator or the domain-wall
fermion.
In this paper we propose an orbifolding projection procedure to impose the
Schroedinger functional Dirichlet boundary condition on the domain-wall
fermion.Comment: 32 page
A pseudospectral matrix method for time-dependent tensor fields on a spherical shell
We construct a pseudospectral method for the solution of time-dependent,
non-linear partial differential equations on a three-dimensional spherical
shell. The problem we address is the treatment of tensor fields on the sphere.
As a test case we consider the evolution of a single black hole in numerical
general relativity. A natural strategy would be the expansion in tensor
spherical harmonics in spherical coordinates. Instead, we consider the simpler
and potentially more efficient possibility of a double Fourier expansion on the
sphere for tensors in Cartesian coordinates. As usual for the double Fourier
method, we employ a filter to address time-step limitations and certain
stability issues. We find that a tensor filter based on spin-weighted spherical
harmonics is successful, while two simplified, non-spin-weighted filters do not
lead to stable evolutions. The derivatives and the filter are implemented by
matrix multiplication for efficiency. A key technical point is the construction
of a matrix multiplication method for the spin-weighted spherical harmonic
filter. As example for the efficient parallelization of the double Fourier,
spin-weighted filter method we discuss an implementation on a GPU, which
achieves a speed-up of up to a factor of 20 compared to a single core CPU
implementation.Comment: 33 pages, 9 figure
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