Skip navigation
Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01gq67jr201
 Title: Sparse Signal Processing with Frame Theory Authors: Mixon, Dustin Advisors: Calderbank, Robert Contributors: Applied and Computational Mathematics Department Subjects: Applied mathematics Issue Date: 2012 Publisher: Princeton, NJ : Princeton University Abstract: Many emerging applications involve sparse signals, and their processing is a subject of active research. We desire a large class of sensing matrices which allow the user to discern important properties of the measured sparse signal. Of particular interest are matrices with the restricted isometry property (RIP). RIP matrices are known to enable efficient and stable reconstruction of sufficiently sparse signals, but the deterministic construction of such matrices has proven very difficult. In this thesis, we discuss this matrix design problem in the context of a growing field of study known as frame theory. In the first two chapters, we build large families of equiangular tight frames and full spark frames, and we discuss their relationship to RIP matrices as well as their utility in other aspects of sparse signal processing. In Chapter 3, we pave the road to deterministic RIP matrices, evaluating various techniques to demonstrate RIP, and making interesting connections with graph theory and number theory. We conclude in Chapter 4 with a coherence-based alternative to RIP, which provides near-optimal probabilistic guarantees for various aspects of sparse signal processing while at the same time admitting a whole host of deterministic constructions. URI: http://arks.princeton.edu/ark:/88435/dsp01gq67jr201 Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog Type of Material: Academic dissertations (Ph.D.) Language: en Appears in Collections: Applied and Computational Mathematics

Files in This Item:
File Description SizeFormat
Mixon_princeton_0181D_10242.pdf665.86 kBAdobe PDF

Items in Dataspace are protected by copyright, with all rights reserved, unless otherwise indicated.