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.
Displaying 1 - 2 of 2
Filtering by
- Creators: Turaga, Pavan
Description
Video denoising has been an important task in many multimedia and computer vision applications. Recent developments in the matrix completion theory and emergence of new numerical methods which can efficiently solve the matrix completion problem have paved the way for exploration of new techniques for some classical image processing tasks. Recent literature shows that many computer vision and image processing problems can be solved by using the matrix completion theory. This thesis explores the application of matrix completion in video denoising. A state-of-the-art video denoising algorithm in which the denoising task is modeled as a matrix completion problem is chosen for detailed study. The contribution of this thesis lies in both providing extensive analysis to bridge the gap in existing literature on matrix completion frame work for video denoising and also in proposing some novel techniques to improve the performance of the chosen denoising algorithm. The chosen algorithm is implemented for thorough analysis. Experiments and discussions are presented to enable better understanding of the problem. Instability shown by the algorithm at some parameter values in a particular case of low levels of pure Gaussian noise is identified. Artifacts introduced in such cases are analyzed. A novel way of grouping structurally-relevant patches is proposed to improve the algorithm. Experiments show that this technique is useful, especially in videos containing high amounts of motion. Based on the observation that matrix completion is not suitable for denoising patches containing relatively low amount of image details, a framework is designed to separate patches corresponding to low structured regions from a noisy image. Experiments are conducted by not subjecting such patches to matrix completion, instead denoising such patches in a different way. The resulting improvement in performance suggests that denoising low structured patches does not require a complex method like matrix completion and in fact it is counter-productive to subject such patches to matrix completion. These results also indicate the inherent limitation of matrix completion to deal with cases in which noise dominates the structural properties of an image. A novel method for introducing priorities to the ranked patches in matrix completion is also presented. Results showed that this method yields improved performance in general. It is observed that the artifacts in presence of low levels of pure Gaussian noise appear differently after introducing priorities to the patches and the artifacts occur at a wider range of parameter values. Results and discussion suggesting future ways to explore this problem are also presented.
ContributorsMaguluri, Hima Bindu (Author) / Li, Baoxin (Thesis advisor) / Turaga, Pavan (Committee member) / Claveau, Claude (Committee member) / Arizona State University (Publisher)
Created2013
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