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- Member of: Barrett, The Honors College Thesis/Creative Project Collection
- Resource Type: Text
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, 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.
ContributorsReynolds, Alexander Bryce (Author) / Gelb, Anne (Thesis director) / Cochran, Douglas (Committee member) / Viswanathan, Adityavikram (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
This thesis focused on understanding how humans visually perceive swarm behavior through the use of swarm simulations and gaze tracking. The goal of this project was to determine visual patterns subjects display while observing and supervising a swarm as well as determine what swarm characteristics affect these patterns. As an ultimate goal, it was hoped that this research will contribute to optimizing human-swarm interaction for the design of human supervisory controllers for swarms. To achieve the stated goals, two investigations were conducted. First, subjects gaze was tracked while observing a simulated swarm as it moved across the screen. This swarm changed in size, disturbance level in the position of the agents, speed, and path curvature. Second, subjects were asked to play a supervisory role as they watched a swarm move across the screen toward targets. The subjects determined whether a collision would occur and with which target while their responses as well as their gaze was tracked. In the case of an observatory role, a model of human gaze was created. This was embodied in a second order model similar to that of a spring-mass-damper system. This model was similar across subjects and stable. In the case of a supervisory role, inherent weaknesses in human perception were found, such as the inability to predict future position of curved paths. These findings are discussed in depth within the thesis. Overall, the results presented suggest that understanding human perception of swarms offers a new approach to the problem of swarm control. The ability to adapt controls to the strengths and weaknesses could lead to great strides in the reduction of operators in the control of one UAV, resulting in a move towards one man operation of a swarm.
ContributorsWhitton, Elena Michelle (Author) / Artemiadis, Panagiotis (Thesis director) / Berman, Spring (Committee member) / Barrett, The Honors College (Contributor) / Mechanical and Aerospace Engineering Program (Contributor)
Created2015-05
Description
Deconvolution of noisy data is an ill-posed problem, and requires some form of regularization to stabilize its solution. Tikhonov regularization is the most common method used, but it depends on the choice of a regularization parameter λ which must generally be estimated using one of several common methods. These methods can be computationally intensive, so I consider their behavior when only a portion of the sampled data is used. I show that the results of these methods converge as the sampling resolution increases, and use this to suggest a method of downsampling to estimate λ. I then present numerical results showing that this method can be feasible, and propose future avenues of inquiry.
ContributorsHansen, Jakob Kristian (Author) / Renaut, Rosemary (Thesis director) / Cochran, Douglas (Committee member) / Barrett, The Honors College (Contributor) / School of Music (Contributor) / Economics Program in CLAS (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2015-05
Description
The world of a hearing impaired person is much different than that of somebody capable of discerning different frequencies and magnitudes of sound waves via their ears. This is especially true when hearing impaired people play video games. In most video games, surround sound is fed through some sort of digital output to headphones or speakers. Based on this information, the gamer can discern where a particular stimulus is coming from and whether or not that is a threat to their wellbeing within the virtual world. People with reliable hearing have a distinct advantage over hearing impaired people in the fact that they can gather information not just from what is in front of them, but from every angle relative to the way they're facing. The purpose of this project was to find a way to even the playing field, so that a person hard of hearing could also receive the sensory feedback that any other person would get while playing video games To do this, visual surround sound was created. This is a system that takes a surround sound input, and illuminates LEDs around the periphery of glasses based on the direction, frequency and amplitude of the audio wave. This provides the user with crucial information on the whereabouts of different elements within the game. In this paper, the research and development of Visual Surround Sound is discussed along with its viability in regards to a deaf person's ability to learn the technology, and decipher the visual cues.
ContributorsKadi, Danyal (Co-author) / Burrell, Nathaneal (Co-author) / Butler, Kristi (Co-author) / Wright, Gavin (Co-author) / Kosut, Oliver (Thesis director) / Bliss, Daniel (Committee member) / Barrett, The Honors College (Contributor) / Electrical Engineering Program (Contributor)
Created2015-05
Description
Foveal sensors employ a small region of high acuity (the foveal region) surrounded by a periphery of lesser acuity. Consequently, the output map that describes their sensory acuity is nonlinear, rendering the vast corpus of linear system theory inapplicable immediately to the state estimation of a target being tracked by such a sensor. This thesis treats the adaptation of the Kalman filter, an iterative optimal estimator for linear-Gaussian dynamical systems, to enable its application to the nonlinear problem of foveal sensing. Results of simulations conducted to evaluate the effectiveness of this algorithm in tracking a target are presented, culminating in successful tracking for motion in two dimensions.
ContributorsSpell, Gregory Paul (Co-author) / Cochran, Douglas (Thesis director) / Morrell, Darryl (Committee member) / Barrett, The Honors College (Contributor) / Electrical Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of Historical, Philosophical and Religious Studies (Contributor)
Created2015-05
Description
China's rapid growth was fueled by an unsustainable method: trade environment for GDP. Air pollution has reached dangerous levels and has taken a serious toll on China's economic progress. The World Bank estimates that in 2013, China lost about 10% of its GDP to pollution. As the cost of burning fossil fuels and public dismay continue to mount, the government is taking steps to reduce carbon emissions and appease the people. The rapidly growing nuclear energy program is one of the energy solutions that China is using to addressing carbon emissions. While China has built a respectable amount of renewable energy capacity (such as wind and solar), much of that capacity is not connected to the power grid. Nuclear energy on the other hand, provides a low-emission alternative that operates independently of weather and sunlight. However, the accelerated pace of reactor construction in recent years presents challenges for the safe operation of nuclear energy in China. It is in China's (and the world's) best interest that a repeat of the Fukushima accident does not occur. In the wake of the Fukushima nuclear accident, public support for nuclear energy in China took a serious hit. A major domestic nuclear accident would be detrimental to the development of nuclear energy in China and diminish the government's reliability in the eyes of the people. This paper will outline those risk factors such as regulatory efforts, legal framework, technological issues, spent fuel disposal, and public perception and provide suggestions to decrease the risk of a major nuclear accident.
ContributorsLiu, Haoran (Author) / Kelman, Jonathan (Thesis director) / Cochran, Douglas (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
In this paper, we propose an autonomous throwing and catching system to be developed as a preliminary step towards the refinement of a robotic arm capable of improving strength and motor function in the limb. This will be accomplished by first autonomizing simpler movements, such as throwing a ball. In this system, an autonomous thrower will detect a desired target through the use of image processing. The launch angle and direction necessary to hit the target will then be calculated, followed by the launching of the ball. The smart catcher will then detect the ball as it is in the air, calculate its expected landing location based on its initial trajectory, and adjust its position so that the ball lands in the center of the target. The thrower will then proceed to compare the actual landing position with the position where it expected the ball to land, and adjust its calculations accordingly for the next throw. By utilizing this method of feedback, the throwing arm will be able to automatically correct itself. This means that the thrower will ideally be able to hit the target exactly in the center within a few throws, regardless of any additional uncertainty in the system. This project will focus of the controller and image processing components necessary for the autonomous throwing arm to be able to detect the position of the target at which it will be aiming, and for the smart catcher to be able to detect the position of the projectile and estimate its final landing position by tracking its current trajectory.
ContributorsLundberg, Kathie Joy (Co-author) / Thart, Amanda (Co-author) / Rodriguez, Armando (Thesis director) / Berman, Spring (Committee member) / Electrical Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
The solution of the linear system of equations $Ax\approx b$ arising from the discretization of an ill-posed integral equation with a square integrable kernel is considered. The solution by means of Tikhonov regularization in which $x$ is found to as the minimizer of $J(x)=\{ \|Ax -b\|_2^2 + \lambda^2 \|L x\|_2^2\}$ introduces the unknown regularization parameter $\lambda$ which trades off the fidelity of the solution data fit and its smoothing norm, which is determined by the choice of $L$. The Generalized Discrepancy Principle (GDP) and Unbiased Predictive Risk Estimator (UPRE) are methods for finding $\lambda$ given prior conditions on the noise in the measurements $b$. Here we consider the case of $L=I$, and hence use the relationship between the singular value expansion and the singular value decomposition for square integrable kernels to prove that the GDP and UPRE estimates yield a convergent sequence for $\lambda$ with increasing problem size. Hence the estimate of $\lambda$ for a large problem may be found by down-sampling to a smaller problem, or to a set of smaller problems, and applying these estimators more efficiently on the smaller problems. In consequence the large scale problem can be solved in a single step immediately with the parameter found from the down sampled problem(s).
ContributorsHorst, Michael Jacob (Author) / Renaut, Rosemary (Thesis director) / Cochran, Douglas (Committee member) / Wang, Yang (Committee member) / Barrett, The Honors College (Contributor) / School of Music (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2014-05
Description
In many systems, it is difficult or impossible to measure the phase of a signal. Direct recovery from magnitude is an ill-posed problem. Nevertheless, with a sufficiently large set of magnitude measurements, it is often possible to reconstruct the original signal using algorithms that implicitly impose regularization conditions on this ill-posed problem. Two such algorithms were examined: alternating projections, utilizing iterative Fourier transforms with manipulations performed in each domain on every iteration, and phase lifting, converting the problem to that of trace minimization, allowing for the use of convex optimization algorithms to perform the signal recovery. These recovery algorithms were compared on a basis of robustness as a function of signal-to-noise ratio. A second problem examined was that of unimodular polyphase radar waveform design. Under a finite signal energy constraint, the maximal energy return of a scene operator is obtained by transmitting the eigenvector of the scene Gramian associated with the largest eigenvalue. It is shown that if instead the problem is considered under a power constraint, a unimodular signal can be constructed starting from such an eigenvector that will have a greater return.
ContributorsJones, Scott Robert (Author) / Cochran, Douglas (Thesis director) / Diaz, Rodolfo (Committee member) / Barrett, The Honors College (Contributor) / Electrical Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2014-05
Description
Passive radar can be used to reduce the demand for radio frequency spectrum bandwidth. This paper will explain how a MATLAB simulation tool was developed to analyze the feasibility of using passive radar with digitally modulated communication signals. The first stage of the simulation creates a binary phase-shift keying (BPSK) signal, quadrature phase-shift keying (QPSK) signal, or digital terrestrial television (DTTV) signal. A scenario is then created using user defined parameters that simulates reception of the original signal on two different channels, a reference channel and a surveillance channel. The signal on the surveillance channel is delayed and Doppler shifted according to a point target scattering profile. An ambiguity function detector is implemented to identify the time delays and Doppler shifts associated with reflections off of the targets created. The results of an example are included in this report to demonstrate the simulation capabilities.
ContributorsScarborough, Gillian Donnelly (Author) / Cochran, Douglas (Thesis director) / Berisha, Visar (Committee member) / Wang, Chao (Committee member) / Barrett, The Honors College (Contributor) / Electrical Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2014-05