Samuel Ginn College of Engineering
http://hdl.handle.net/11200/554
2017-02-27T21:57:58ZA Solution of Rigid Perfectly Plastic Deep Spherical Indentation based on Slip Line Theory
http://hdl.handle.net/11200/48538
A Solution of Rigid Perfectly Plastic Deep Spherical Indentation based on Slip Line Theory
During indentation it is often important to determine the relationship between the average pressure and the yield strength. This work uses slip line theory to determine this relationship for the case of a rigid sphere indenting a frictionless perfectly plastic half-space (i.e. no hardening). The results show that the ratio between the average contact pressure and the yield strength decreases as the depth of indentation is increased. Note that the slip-line analysis does not include the effects of pile-up or sink-in deformations. However, the slip-line theory has also been compared to data generated using the finite element method (FEM). The theory and the FEM results appear to agree well.
2015-11-16T00:00:00ZTrust region methods for estimation of a complex exponential decay model in MRI with a single-shot or multi-shot trajectory (in review)
http://hdl.handle.net/11200/48506
Trust region methods for estimation of a complex exponential decay model in MRI with a single-shot or multi-shot trajectory (in review)
Joint estimation of spin density, R2* decay and off-resonance frequency maps is very useful in many magnetic resonance imaging (MRI) applications. The standard multi-echo approach can achieve high accuracy but requires a long acquisition time for sampling multiple k-space frames. There are many approaches to accelerate the acquisition. Among them, single- or multi-shot trajectory based sampling has recently drawn attention due to its fast data acquisition. However, this sampling strategy destroys the Fourier relationship between k-space and images, leading to a great challenge for the reconstruction. In this work, we present two trust region methods based on two different linearization strategies for the nonlinear signal model. A trust region is defined as a local area in the variable space where a local linear approximation is trustable. In each iteration, the method minimizes a local approximation within a trust region so that the step size can be kept in a suitable scale. A continuation scheme is applied to gradually reduce the regularization over the parameter maps and facilitate convergence from poor initializations. The two trust region methods are compared to two other previously proposed methods---the nonlinear conjugate gradients and the gradual refinement algorithm. Experiments based on various synthetic data and real phantom data show that the two trust region methods have a clear advantage in both speed and stability.
2015-05-05T00:00:00ZAn efficient auxiliary variable method for quantification of spin density, R2* decay and field inhomogeneity maps in magnetic resonance imaging
http://hdl.handle.net/11200/48505
An efficient auxiliary variable method for quantification of spin density, R2* decay and field inhomogeneity maps in magnetic resonance imaging
Quantification of spin density, $R_2^*$ decay and off-resonance frequency maps is very important in some applications of magnetic resonance imaging (MRI). To reconstruct these parameter maps, a time-varying model such as mono-exponentials must be used to represent the signal from each voxel. When only a single-shot trajectory is adopted, the underlying reconstruction problem is significantly nonlinear and therefore requires an iterative algorithm. The regularized trust region method previously proposed to address this problem is stable but lacks speed. In this paper, we propose a novel auxiliary variable method that is very efficient in solving the underlying optimization problem. This method introduces an auxiliary variable in the spatial-temporal domain that separates the data fidelity term and the structure fidelity term. The algorithm then alternately optimizes the data fidelity and the structure fidelity to reach the solution. The data fidelity optimization has a closed-form solution and can be solved very efficiently. The structure fidelity optimization fits the exponential model with the auxiliary variable and can also be rapidly computed. Some preliminary comparisons between the auxiliary variable method and the trust region method show that the new method is 10 times faster than the trust region method at a reasonable reconstruction precision.
2015-04-07T00:00:00ZCharacterization of Plenoptic Imaging Systems and Efficient Volumetric Estimation from Plenoptic Data
http://hdl.handle.net/11200/48467
Characterization of Plenoptic Imaging Systems and Efficient Volumetric Estimation from Plenoptic Data
Plenoptic imaging is a rapidly growing field driven
by the ever-declining cost of imaging systems and the promise
of image focus, perspective, and depth of field manipulation
during post-processing. While plenoptic systems are often limited
to 2D image reconstruction and manipulation, plenoptic data
and reconstruction algorithms can be extended to volumetric
fields. An estimate of the imaged volume can be created by
generating a stack of 2D images, but such an estimate can easily
be dominated by image blur from neighboring focal planes.
Tomographic algorithms have been shown to be effective in
creating volumetric estimates from plenoptic data but are often
prohibitively slow. The research presented here shows that the
reconstruction is solvable through deconvolution. Unfortunately,
the observation model is not shift-invariant. However, with
appropriate transformations, the problem can be made shiftinvariant
so that deconvolution is a viable solution. Utilizing the
computationally efficient fast Fourier transform (FFT) allows the
reconstruction to be completed quickly while producing estimates
exhibiting significantly reduced blur compared to a simple focal
stack. This work describes a deconvolution algorithm designed
to reconstruct a 3D volume from a 2D plenoptic image. The
imaging system and refocusing algorithm are characterized with
respect to shift-variance in order to identify potential sources of
artifacts and propose potential mitigating steps. To demonstrate
the efficacy of the algorithm, experimental data is presented with
comparisons of the focal stack to the reconstructed volume.
2015-01-13T00:00:00Z