Matching Items (4)

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Designing concentration factors to detect jump discontinuities from non-uniform Fourier data

Description

Edge detection plays a significant role in signal processing and image reconstruction applications where it is used to identify important features in the underlying signal or image. In some of

Edge detection plays a significant role in signal processing and image reconstruction applications where it is used to identify important features in the underlying signal or image. In some of these applications, such as magnetic resonance imaging (MRI), data are sampled in the Fourier domain. When the data are sampled uniformly, a variety of algorithms can be used to efficiently extract the edges of the underlying images. However, in cases where the data are sampled non-uniformly, such as in non-Cartesian MRI, standard inverse Fourier transformation techniques are no longer suitable. Methods exist for handling these types of sampling patterns, but are often ill-equipped for cases where data are highly non-uniform. This thesis further develops an existing approach to discontinuity detection, the use of concentration factors. Previous research shows that the concentration factor technique can successfully determine jump discontinuities in non-uniform data. However, as the distribution diverges further away from uniformity so does the efficacy of the identification. This thesis proposes a method for reverse-engineering concentration factors specifically tailored to non-uniform data by employing the finite Fourier frame approximation. Numerical results indicate that this design method produces concentration factors which can more precisely identify jump locations than those previously developed.

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Date Created
  • 2015-05

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Edge Detection from Spectral Phase Data

Description

The detection and characterization of transients in signals is important in many wide-ranging applications from computer vision to audio processing. Edge detection on images is typically realized using small, local,

The detection and characterization of transients in signals is important in many wide-ranging applications from computer vision to audio processing. Edge detection on images is typically realized using small, local, discrete convolution kernels, but this is not possible when samples are measured directly in the frequency domain. The concentration factor edge detection method was therefore developed to realize an edge detector directly from spectral data. This thesis explores the possibilities of detecting edges from the phase of the spectral data, that is, without the magnitude of the sampled spectral data. Prior work has demonstrated that the spectral phase contains particularly important information about underlying features in a signal. Furthermore, the concentration factor method yields some insight into the detection of edges in spectral phase data. An iterative design approach was taken to realize an edge detector using only the spectral phase data, also allowing for the design of an edge detector when phase data are intermittent or corrupted. Problem formulations showing the power of the design approach are given throughout. A post-processing scheme relying on the difference of multiple edge approximations yields a strong edge detector which is shown to be resilient under noisy, intermittent phase data. Lastly, a thresholding technique is applied to give an explicit enhanced edge detector ready to be used. Examples throughout are demonstrate both on signals and images.

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Date Created
  • 2016-05

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Edge Detection from Non-Uniform Fourier Data via a Modified Method of Convolutional Gridding

Description

The recovery of edge information in the physical domain from non-uniform Fourier data is of importance in a variety of applications, particularly in the practice of magnetic resonance imaging (MRI).

The recovery of edge information in the physical domain from non-uniform Fourier data is of importance in a variety of applications, particularly in the practice of magnetic resonance imaging (MRI). Edge detection can be important as a goal in and of itself in the identification of tissue boundaries such as those defining the locations of tumors. It can also be an invaluable tool in the amelioration of the negative effects of the Gibbs phenomenon on reconstructions of functions with discontinuities or images in multi-dimensions with internal edges. In this thesis we develop a novel method for recovering edges from non-uniform Fourier data by adapting the "convolutional gridding" method of function reconstruction. We analyze the behavior of the method in one dimension and then extend it to two dimensions on several examples.

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Date Created
  • 2013-05

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Characterizing pressure induced structural changes in glasses and liquids

Description

The behaviors of various amorphous materials are characterized at high pressures to deduce phase transitions, coordination changes, densification, and other structural or electronic alterations in the system. Alongside, improvements on

The behaviors of various amorphous materials are characterized at high pressures to deduce phase transitions, coordination changes, densification, and other structural or electronic alterations in the system. Alongside, improvements on high pressure techniques are presented to measure equations of state of glassy materials and probe liquids using in-situ high resolution nuclear magnetic resonance (NMR) spectroscopy. 27Al NMR is used to quantify coordination changes in CaAl2O4 glass pressure cycled to 16 GPa. The structure and coordination environments remain unchanged up to 8 GPa at which 93% of the recovered glass exists as 4-fold Al, whereas the remaining population exists as [5,6]Al. Upon densification, [5,6]Al comprise nearly 30% of observed Al, most likely through the generation of 3-coordinated oxygen. A method to determine the volumetric equation of state of amorphous solids using optical microscopy in a diamond anvil cell is also described. The method relies on two dimensional image acquisition and analysis to quantify changes in the projected image area with compression. The area analysis method is used to determine the compression of cubic crystals, yielding results in good agreement with diffraction and volumetric measurements. A NMR probe capable of reaching 3 GPa is built to understand the nature of magnetic field gradients and improve upon the resolution of high pressure studies conducted in a diamond anvil cell. Field gradients in strength up to 6 G/cm are caused largely by mismatches in the magnetic susceptibility between the sample and gasket, which is proven to shift the chemical shift distribution by use of several different metallic gaskets. Polyamorphic behavior in triphenyl phosphite is studied at pressures up to 0.7 GPa to elucidate the formation of the glacial phase at high pressures. A perceived liquid-liquid phase transition is shown to follow a positive Clapeyron slope, and closely follows the predicted glass transition line up to 0.4 GPa and temperatures below 270 K. A drastic change in morphology is indicative of a transformation from liquid I to liquid II and followed by optical microscopy.

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Date Created
  • 2012