說明 
269 p 
附註 
Source: Dissertation Abstracts International, Volume: 6803, Section: B, page: 1846 

Adviser: Richard G. Baraniuk 

Thesis (Ph.D.)Rice University, 2007 

Models in signal processing often deal with some notion of structure or conciseness suggesting that a signal really has "few degrees of freedom" relative to its actual size. Examples include: bandlimited signals, images containing lowdimensional geometric features, or collections of signals observed from multiple viewpoints in a camera or sensor network. In many cases, such signals can be expressed as sparse linear combinations of elements from some dictionarythe sparsity of the representation directly reflects the conciseness of the model and permits efficient algorithms for signal processing. Sparsity also forms the core of the emerging theory of Compressed Sensing (CS), which states that a sparse signal can be recovered from a small number of random linear measurements 

In other cases, however, sparse representations may not suffice to truly capture the underlying structure of a signal. Instead, the conciseness of the signal model may in fact dictate that the signal class forms a lowdimensional manifold as a subset of the highdimensional ambient signal space. To date, the importance and utility of manifolds for signal processing has been acknowledged largely through a research effort into "learning" manifold structure from a collection of data points. While these methods have proved effective for certain tasks (such as classification and recognition), they also tend to be quite generic and fail to consider the geometric nuances of specific signal classes 

The purpose of this thesis is to develop new methods and understanding for signal processing based on lowdimensional signal models, with a particular focus on the role of geometry. Our key contributions include (i) new models for lowdimensional signal structure, including local parametric models for piecewise smooth signals and joint sparsity models for signal collections; (ii) multiscale representations for piecewise smooth signals designed to accommodate efficient processing; (iii) insight and analysis into the geometry of lowdimensional signal models, including the nondifferentiability of certain articulated image manifolds and the behavior of signal manifolds under random lowdimensional projections, and (iv) dimensionality reduction algorithms for image approximation and compression, distributed (multisignal) CS, parameter estimation, manifold learning, and manifoldbased CS 

School code: 0187 

DDC 
Host Item 
Dissertation Abstracts International 6803B

主題 
Applied Mechanics


Engineering, Electronics and Electrical


0346


0544

Alt Author 
Rice University

