University of Central Florida
Spectrally Uniform Frames And Spectrally Optimal Dual Frames.
Degree: 2013, University of Central Florida
Frames have been useful in signal transmission due to the built in redundancy. In recent years, the erasure problem in data transmission has been the focus of considerable research in the case the error estimate is measured by operator (or matrix) norm. Sample results include the characterization of one-erasure optimal Parseval frames, the connection between two-erasure optimal Parseval frames and equiangular frames, and some characterization of optimal dual frames. If iterations are allowed in the reconstruction process of the signal vector, then spectral radius measurement for the error operators is more appropriate then the operator norm measurement. We obtain a complete characterization of spectrally one-uniform frames (i.e., one-erasure optimal frames with respect to the spectral radius measurement) in terms of the redundancy distribution of the frame. Our characterization relies on the connection between spectrally optimal frames and the linear connectivity property of the frame. We prove that the linear connectivity property is equivalent to the intersection dependence property, and is also closely related to the well-known concept of k-independent set. For spectrally two-uniform frames, it is necessary that the frame must be linearly connected. We conjecture that it is also necessary that a two-uniform frame must be n-independent. We confirmed this conjecture for the case when N = n+1, n+2, where N is the number of vectors in a frame for an n-dimensional Hilbert space. Additionally we also establish several necessary and sufficient conditions for the existence of an alternate dual frame to make the iii iterated reconstruction to work.
Advisors/Committee Members: Han, Deguang.
Subjects/Keywords: Frames; optimal dual frames; spectrally uniform frames; spectrally optimal dual frames; Mathematics; Dissertations, Academic – Sciences, Sciences – Dissertations, Academic
to Zotero / EndNote / Reference
APA (6th Edition):
Pehlivan, S. (2013). Spectrally Uniform Frames And Spectrally Optimal Dual Frames. (Doctoral Dissertation). University of Central Florida. Retrieved from https://stars.library.ucf.edu/etd/2724
Chicago Manual of Style (16th Edition):
Pehlivan, Saliha. “Spectrally Uniform Frames And Spectrally Optimal Dual Frames.” 2013. Doctoral Dissertation, University of Central Florida. Accessed September 23, 2019.
MLA Handbook (7th Edition):
Pehlivan, Saliha. “Spectrally Uniform Frames And Spectrally Optimal Dual Frames.” 2013. Web. 23 Sep 2019.
Pehlivan S. Spectrally Uniform Frames And Spectrally Optimal Dual Frames. [Internet] [Doctoral dissertation]. University of Central Florida; 2013. [cited 2019 Sep 23].
Available from: https://stars.library.ucf.edu/etd/2724.
Council of Science Editors:
Pehlivan S. Spectrally Uniform Frames And Spectrally Optimal Dual Frames. [Doctoral Dissertation]. University of Central Florida; 2013. Available from: https://stars.library.ucf.edu/etd/2724