Auburn University Graduate School
http://hdl.handle.net/10415/1
2019-05-26T09:00:32ZPathways of Dysregulation: The Influence of Lifetime Poly-Victimization on Therapy-Interfering Psychosocial Impairment in Adolescents Adjudicated for Sex Offenses
http://hdl.handle.net/10415/6740
Pathways of Dysregulation: The Influence of Lifetime Poly-Victimization on Therapy-Interfering Psychosocial Impairment in Adolescents Adjudicated for Sex Offenses
Harrelson, Megan, E.
The preset study examined the relationship between poly-victimization exposure, affective dysregulation, and three negative psychosocial outcomes: externalizing problems, posttraumatic stress, and suicidal behavior. Adolescents adjudicated for sex offenses are a poly-victimized population who display psychosocial impairment tied to maladaptive affective regulatory strategies. If left untreated, functional impairment can interfere with the remediation of illegal sexual behaviors. Participants consisted of 165 adolescent males enrolled in mandated residential treatment following a sex offense. Childhood poly-victimization exposure and affective dysregulation severity were expected to predict psychosocial impairment. Affective dysregulation was also expected to partially mediate the relationships between poly-victimization and externalizing problems, posttraumatic stress, and suicidal behavior. Consistent with the main hypothesis, a significant indirect effect was observed between poly-victimization and all three areas of psychosocial impairment via affective dysregulation. Findings highlight the impact of poly-victimization exposure on functional impairment, as well as the importance of assessing for multiple types of victimization in adolescents who engage in illegal sexual behavior. Clinical implications regarding the use of trauma-informed approaches during sex offender treatment are discussed.
2019-05-22T00:00:00ZEfficient Algorithms for Retrospective Motion Correction in MRI
http://hdl.handle.net/10415/6739
Efficient Algorithms for Retrospective Motion Correction in MRI
Bian, Yuan
Compared with other medical imaging modalities, MR imaging is time consuming due to the relatively slow sequential data acquisition pattern. Hence, motion is often an unavoidable issue for MRI. Object motion during the signal acquisition can reduce image quality due to the induced artifacts, which further hinders diagnosis and scientific research. These degraded images may require repeated scans, which leads to treatment delay and cost increases. If images with motion artifacts are not properly interpreted, erroneous diagnoses and false scientific findings may occur.
To reduce motion artifacts, three groups of methods are used by practitioners: motion prevention, artifact mitigation, and motion correction. Motion prevention methods are the most straightforward way to reduce motion artifacts. However, these may not always be suitable or effective. Artifact mitigation methods mainly include faster imaging and periodic triggering and gating. Imaging speed has limits, and triggering and gating require extra time, effort, and complexity. Therefore, motion correction methods have received significant attention.
MRI motion correction techniques can be classified into three groups: motion correction based on k-space trajectories, prospective motion correction (PMC) and retrospective motion correction (RMC). Motion correction based on k-space trajectories relies on specially designed and implemented trajectories, which limits the flexibility of the techniques and requires more acquisition time. PMC is achieved by obtaining tracking data of the pose (position and orientation) of the object, passing these data to the scanner with minimal delay, and adjusting the MR pulse sequences so that the imaging volume moves to follow the object. PMC requires extra hardware and calibration and sometimes extra acquisition time. RMC postprocesses the data and reconstructs MR images after the data is fully acquired. In RMC the process of acquisition is independent of motion. RMC includes three main groups: self-navigation motion tracking methods to calculate motion information, autofocusing methods based on evaluation of image quality, and motion correction by training neural networks. Self-navigation motion correction methods rely on Fourier properties by taking advantage of overlapping k-space data to track motion. This approach requires additional k-trajectories, which increases both time and complexity of the scan. Autofocusing methods do not rely on a specific data sample pattern, equipment or sequence design. These approaches assume a rigid body or deformable object motion model and estimate motion model parameters by iterative optimization of an image quality metric when the raw k-space data are modified according to the motion model. Artificial neural network methods establish the mapping relationship between the motion-corrupted images and the no-motion images by training a large number of related images, and estimate motion-corrected images from motion-corrupted images. The focus of this thesis is the development of autofocusing and neural-network approaches to RMC.
In this dissertation, we develop three methods to correct MRI motion retrospectively. The first contribution is an autofocusing motion correction method to address the two challenges of previous methods: high calculation load and local minima. We propose to use multiple linear-motion initializations and joint refinement of a global model to decrease and constrain the search space. In the first step, k-space is divided into several segments based on acquisition order. Linear motion is assumed and searched in each segment to get initial motion parameters. In the second step, several control points are chosen on the piecewise linear initial approximation, and then a piecewise cubic Hermite interpolation polynomial is fitted from the control points to obtain smooth motion curves. The motion curves are refined by optimizing a focus criterion. These strategies make the proposed algorithm efficient and robust. Different focus criteria are compared under the proposed method. To further improve computational efficiency, golden-section search is used to estimate rotation, and two map data structures are applied to store calculated data. Simulations and experimental results demonstrate that the proposed method can effectively and efficiently correct rigid motion in MR images.
The second contribution of this work is an efficient motion correction method based on fast robust correlation. Translational search can be computationally demanding. A correlation operation can be used to calculate an image match when the matching criterion is the sum of squared errors. However, this approach cannot be used for nonquadratic matching criteria. Fast robust correlation is a computationally efficient search algorithm for translational image matching in the frequency domain. This method can calculate matching surfaces from nonquadratic criteria using a series of high-speed correlations by defining a kernel with sinusoidal terms. The proposed method corrects motion-distorted images by aligning translational motion between images formed by neighboring frequency segments. Since the squared difference kernel is invariant to motion between partial-Fourier images, we adopt the absolute value kernel, which can be easily approximated by sinusoidal terms. Total variation of the sum of partial-Fourier images is chosen as the new matching criterion. FFTs are used to calculate correlations for computational speed. Different search strategies to combine and correct motion over the whole k-space are discussed and compared. The proposed method can perform real-time processing to reduce image motion artifacts significantly in the simulations and MRI cardiac experiments.
The third contribution of this dissertation is a novel data-driven motion correction method for magnitude MR images using generative adversarial networks (GANs). Although the previous proposed methods can correct motion effectively and efficiently, they both require complex-valued raw data. However, raw data is not usually preserved in a clinical environment. In this case the previous two methods cannot be used. GANs (pix2pix model) are implemented to reduce motion artifacts and reconstruct motion-corrupted images through adversarial training between generator and discriminator networks to estimate a motion-corrected image that is close to the reference image. The training set is made of image pairs consisting of motionless reference images and corresponding motion-simulated images. The proposed method is validated by a simulated motion test set and a real motion (experimental) test set.
2019-05-22T00:00:00ZOn The Number of Cylinders Touching a Sphere
http://hdl.handle.net/10415/6738
On The Number of Cylinders Touching a Sphere
Yardimci, Osman
The kissing number problem is a packing problem in geometry where one has to find
the maximum number of congruent non-overlapping copies of a given body so that they can
be arranged each touching a common copy.
The most studied version of this problem is about the kissing number of the unit ball.
A similar question was proposed by Wlodzimierz Kuperberg in 1990. Kuperberg asked
for the maximum number of non-overlapping infinitely long unit cylinders touching a unit
ball. He conjectured that at most six disjoint in finitely long unit cylinders can touch a unit
sphere. W. Kuperberg's so called six cylinder problem [WK90] is a well known, 28 year old
problem in discrete geometry and it is still an open problem.
In 2015, Moritz Firsching showed an arrangement of 6 disjoint cylinders with radii
1.0496594, where each cylinder touched a given unit ball.
In this dissertation several variants of W. Kuperberg's problem are considered and
solved. For example new bounds will be proved concerning the number of tangent cylinders
with various radii. Some already known bounds will be improved by elaborating on the
method introduced by Brass and Wenk [BW00]. Application of a deep theorem on circle
packing by Musin [OM03] also provides some non-trivial bounds. The major part of the
dissertation is about proving theorems concerning the size and the number of discs which
one can place on a concentric sphere avoiding the cylinders. This way new lower bounds are
proved for the total area between cylinders on a concentric sphere. Such lower bounds can
improve the existing results concerning Kuperberg's type cylinder problems. Most of the
lemmas will be proved with pure geometric arguments, but in some cases the final answer
uses Maple computations. We give several different lower bounds for the total area of gaps.
Even our best lower bound does not solve Kuperberg's 6 cylinder problem. The last section
contains an application of our lower bound (joint work with Andras Bezdek) where it is
proved that seven infinitely long cylinders of radii 1.04965 (Firsching's radius) cannot touch
a unit sphere. In view of Firsching's construction this settles the Kuperberg question for
radius 1.04965.
2019-05-21T00:00:00ZPedestrian Navigation using Particle Filtering and a priori Building Maps
http://hdl.handle.net/10415/6737
Pedestrian Navigation using Particle Filtering and a priori Building Maps
Ray, Tanner
This thesis presents a new particle filter (PF) weight update method that improves the performance of indoor positioning systems. In standalone inertial pedestrian-dead-reckoning (PDR) systems, the position error grows with time due to the inertial measurement unitâ€™s (IMU) sensor errors. Often external measurements from GPS or radio networks (e.g. wireless local area network (WLAN), ultra-wide-band (UWB), Bluetooth low energy (BLE) etc.) are used to restrict the error growth. External measurements from infrastructure-based systems have inherent high costs and deployment time, thus they are not easily implemented. The presented work focuses on the development of a standalone wearable navigation system that does not depend on physical infrastructure. In order to constrain error growth without external measure- ments, other techniques that have been developed that utilize building map information as a measurement. One method uses the building to provide a heading measurement to reduce the drift in the heading solution. This is based upon the behavior that pedestrians when walking in building corridors typically walk straight. Another method constrains the error based upon the knowledge that pedestrian motion is limited by building floorplans, (e.g. walls, floors, and other features). This technique uses PF estimation to fuse standalone PDR with map measure- ments to perform accurate pedestrian localization. These techniques along with the current PDR techniques and underlying algorithms are discussed in detail. Lastly, this work presents a comparison of PFs that utilize different particle propagation and weight update methods for indoor positioning systems. A new type of weight update is also introduced that provides a more accurate localization. A performance evaluation with simulated and experimental data, showed improved performance using the new weight update. The results of this and a summary are provided.
2019-05-16T00:00:00Z