Felix Ackermann
Redundancy of finite frames with a discussion on Gabor frames = /.
Rel. Bengt Patrik Martin Wahlberg. Politecnico di Torino, Corso di laurea magistrale in Ingegneria Matematica, 2022
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Abstract
Frames represent an important theoretical concept for signal processing. A frame is a collection of vectors satisfying the frame inequality, i.e. a relaxed form of Parseval’s identity for which the vectors involved do not need to form an orthonormal basis. Frames are used in order to provide a redundant representation of a vector (signal) in terms of coefficients associated to the frame’s elements. The goal of this thesis is to quantify redundancy for frames. Therefore we present a combinatorial- and an analytical redundancy measure. Both yield information on the maximal number of spanning sets and the minimal number of linearly independent sets one can partition the frame into, though in general the two measures are not equivalent.
For the combinatorial measure we show a proof of the Rado-Horn theorem and two results basing upon it
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