282 research outputs found
X-ray CT Image Reconstruction on Highly-Parallel Architectures.
Model-based image reconstruction (MBIR) methods for X-ray CT use accurate
models of the CT acquisition process, the statistics of the noisy measurements,
and noise-reducing regularization to produce potentially higher quality images
than conventional methods even at reduced X-ray doses. They do this by
minimizing a statistically motivated high-dimensional cost function; the high
computational cost of numerically minimizing this function has prevented MBIR
methods from reaching ubiquity in the clinic. Modern highly-parallel hardware
like graphics processing units (GPUs) may offer the computational resources to
solve these reconstruction problems quickly, but simply "translating" existing
algorithms designed for conventional processors to the GPU may not fully
exploit the hardware's capabilities.
This thesis proposes GPU-specialized image denoising and image reconstruction
algorithms. The proposed image denoising algorithm uses group coordinate
descent with carefully structured groups. The algorithm converges very
rapidly: in one experiment, it denoises a 65 megapixel image in about 1.5
seconds, while the popular Chambolle-Pock primal-dual algorithm running on the
same hardware takes over a minute to reach the same level of accuracy.
For X-ray CT reconstruction, this thesis uses duality and group coordinate
ascent to propose an alternative to the popular ordered subsets (OS) method.
Similar to OS, the proposed method can use a subset of the data to update the
image. Unlike OS, the proposed method is convergent. In one helical CT
reconstruction experiment, an implementation of the proposed algorithm using
one GPU converges more quickly than a state-of-the-art algorithm converges
using four GPUs. Using four GPUs, the proposed algorithm reaches near
convergence of a wide-cone axial reconstruction problem with over 220 million
voxels in only 11 minutes.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/113551/1/mcgaffin_1.pd
Symmetry-Adapted Phonon Analysis of Nanotubes
The characteristics of phonons, i.e. linearized normal modes of vibration,
provide important insights into many aspects of crystals, e.g. stability and
thermodynamics. In this paper, we use the Objective Structures framework to
make concrete analogies between crystalline phonons and normal modes of
vibration in non-crystalline but highly symmetric nanostructures. Our strategy
is to use an intermediate linear transformation from real-space to an
intermediate space in which the Hessian matrix of second derivatives is
block-circulant. The block-circulant nature of the Hessian enables us to then
follow the procedure to obtain phonons in crystals: namely, we use the Discrete
Fourier Transform from this intermediate space to obtain a block-diagonal
matrix that is readily diagonalizable. We formulate this for general Objective
Structures and then apply it to study carbon nanotubes of various chiralities
that are subjected to axial elongation and torsional deformation. We compare
the phonon spectra computed in the Objective Framework with spectra computed
for armchair and zigzag nanotubes. We also demonstrate the approach by
computing the Density of States. In addition to the computational efficiency
afforded by Objective Structures in providing the transformations to
almost-diagonalize the Hessian, the framework provides an important conceptual
simplification to interpret the phonon curves.Comment: To appear in J. Mech. Phys. Solid
The symmetries of octupolar tensors
Octupolar tensors are third order, completely symmetric and traceless
tensors. Whereas in 2D an octupolar tensor has the same symmetries as an
equilateral triangle and can ultimately be identified with a vector in the
plane, the symmetries that it enjoys in 3D are quite different, and only
exceptionally reduce to those of a regular tetrahedron. By use of the octupolar
potential that is, the cubic form associated on the unit sphere with an
octupolar tensor, we shall classify all inequivalent octupolar symmetries. This
is a mathematical study which also reviews and incorporates some previous, less
systematic attempts
Nonlinear Dynamics
This volume covers a diverse collection of topics dealing with some of the fundamental concepts and applications embodied in the study of nonlinear dynamics. Each of the 15 chapters contained in this compendium generally fit into one of five topical areas: physics applications, nonlinear oscillators, electrical and mechanical systems, biological and behavioral applications or random processes. The authors of these chapters have contributed a stimulating cross section of new results, which provide a fertile spectrum of ideas that will inspire both seasoned researches and students
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