Theses and Dissertations
This collection includes both ASU Theses and Dissertations, submitted by graduate students, and the Barrett, Honors College theses submitted by undergraduate students.
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- Creators: Turaga, Pavan
Description
As the application of interactive media systems expands to address broader problems in health, education and creative practice, they fall within a higher dimensional space for which it is inherently more complex to design. In response to this need an emerging area of interactive system design, referred to as experiential media systems, applies hybrid knowledge synthesized across multiple disciplines to address challenges relevant to daily experience. Interactive neurorehabilitation (INR) aims to enhance functional movement therapy by integrating detailed motion capture with interactive feedback in a manner that facilitates engagement and sensorimotor learning for those who have suffered neurologic injury. While INR shows great promise to advance the current state of therapies, a cohesive media design methodology for INR is missing due to the present lack of substantial evidence within the field. Using an experiential media based approach to draw knowledge from external disciplines, this dissertation proposes a compositional framework for authoring visual media for INR systems across contexts and applications within upper extremity stroke rehabilitation. The compositional framework is applied across systems for supervised training, unsupervised training, and assisted reflection, which reflect the collective work of the Adaptive Mixed Reality Rehabilitation (AMRR) Team at Arizona State University, of which the author is a member. Formal structures and a methodology for applying them are described in detail for the visual media environments designed by the author. Data collected from studies conducted by the AMRR team to evaluate these systems in both supervised and unsupervised training contexts is also discussed in terms of the extent to which the application of the compositional framework is supported and which aspects require further investigation. The potential broader implications of the proposed compositional framework and methodology are the dissemination of interdisciplinary information to accelerate the informed development of INR applications and to demonstrate the potential benefit of generalizing integrative approaches, merging arts and science based knowledge, for other complex problems related to embodied learning.
ContributorsLehrer, Nicole (Author) / Rikakis, Thanassis (Committee member) / Olson, Loren (Committee member) / Wolf, Steven L. (Committee member) / Turaga, Pavan (Committee member) / Arizona State University (Publisher)
Created2014
Recursive Bayesian Estimation on Projective Spaces: Theoretical Foundations and Practical Algorithms
Description
This thesis develops geometrically and statistically rigorous foundations for multivariate analysis and bayesian inference posed on grassmannian manifolds. Requisite to the development of key elements of statistical theory in a geometric realm are closed-form, analytic expressions for many differential geometric objects, e.g., tangent vectors, metrics, geodesics, volume forms. The first part of this thesis is devoted to a mathematical exposition of these. In particular, it leverages the classical work of Alan James to derive the exterior calculus of differential forms on special grassmannians for invariant measures with respect to which integration is permissible. Motivated by various multi-sensor remote sensing applications, the second part of this thesis describes the problem of recursively estimating the state of a dynamical system propagating on the Grassmann manifold. Fundamental to the bayesian treatment of this problem is the choice of a suitable probability distribution to a priori model the state. Using the Method of Maximum Entropy, a derivation of maximum-entropy probability distributions on the state space that uses the developed geometric theory is characterized. Statistical analyses of these distributions, including parameter estimation, are also presented. These probability distributions and the statistical analysis thereof are original contributions. Using the bayesian framework, two recursive estimation algorithms, both of which rely on noisy measurements on (special cases of) the Grassmann manifold, are the devised and implemented numerically. The first is applied to an idealized scenario, the second to a more practically motivated scenario. The novelty of both of these algorithms lies in the use of thederived maximumentropy probability measures as models for the priors. Numerical simulations demonstrate that, under mild assumptions, both estimation algorithms produce accurate and statistically meaningful outputs. This thesis aims to chart the interface between differential geometry and statistical signal processing. It is my deepest hope that the geometric-statistical approach underlying this work facilitates and encourages the development of new theories and new computational methods in geometry. Application of these, in turn, will bring new insights and bettersolutions to a number of extant and emerging problems in signal processing.
ContributorsCrider, Lauren N (Author) / Cochran, Douglas (Thesis advisor) / Kotschwar, Brett (Committee member) / Scharf, Louis (Committee member) / Taylor, Thomas (Committee member) / Turaga, Pavan (Committee member) / Arizona State University (Publisher)
Created2021