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Edge Detection from Spectral Phase Data

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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

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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2016-05

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

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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

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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2015-05

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Observability methods in sensor scheduling

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Modern measurement schemes for linear dynamical systems are typically designed so that different sensors can be scheduled to be used at each time step. To determine which sensors to use, various metrics have been suggested. One possible such metric is

Modern measurement schemes for linear dynamical systems are typically designed so that different sensors can be scheduled to be used at each time step. To determine which sensors to use, various metrics have been suggested. One possible such metric is the observability of the system. Observability is a binary condition determining whether a finite number of measurements suffice to recover the initial state. However to employ observability for sensor scheduling, the binary definition needs to be expanded so that one can measure how observable a system is with a particular measurement scheme, i.e. one needs a metric of observability. Most methods utilizing an observability metric are about sensor selection and not for sensor scheduling. In this dissertation we present a new approach to utilize the observability for sensor scheduling by employing the condition number of the observability matrix as the metric and using column subset selection to create an algorithm to choose which sensors to use at each time step. To this end we use a rank revealing QR factorization algorithm to select sensors. Several numerical experiments are used to demonstrate the performance of the proposed scheme.

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2015