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Some Problems on Finite Frames

Author: WangRong
Tutor: GuQing
School: East China Normal University
Course: Operational Research and Cybernetics
Keywords: finite frame ellipsoidal tight frames(ETF) overcomplete frame
CLC: O177.1
Type: Master's thesis
Year: 2006
Downloads: 7
Quote: 0
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Abstract


The theory of frames for a Hilbert.space plays a fundemental role in signal processing, image processing, data compression, robust data transmission and more. Every "real-life" application of frames has to be performed in a finite-dimensional real or complex Hilbert space R~N or C~N(which we denote H_N). As an improvement of a basis, finite frame in a finite-dimensional Hilbert space H_N shows a great value in theory and applications. In this paper, we focus on several problems about finite frames:1. We discuss the construction and characterization of tight frames with length M(M ≥ N) and whose elements lie on an arbitrary ellipsoidal surface ε_T within a finite-dimentional Hilbert space H_N. We prove ε_T contains uncountable ellipsoidal tight frames(ETF) when some conditions are satisfied.2. We discuss the change in frame bounds for an overcomplete frame in H_N after several elements are erased.

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Functional Analysis > Hilbert space and linear operator theory
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