To date, frames have established themselves as a standard notion in applied mathematics,
computer science, and engineering as a means to derive redundant, yet stable …

This book gives a unified introduction to the rapidly developing area of finite tight frames.
Fifteen years ago, the existence of equal-norm tight frames of n> d vectors for Rd and Cd …

We show that much of the theory of finite tight frames can be generalised to vector spaces
over the quaternions. This includes the variational characterisation, group frames, and the …

In this paper we study the properties of multiplication invariant (MI) operators acting on
subspaces of the vector-valued space L 2 (X; H). We characterize such operators in terms of …

Many applications of finite tight frames (eg, the use of SICs and mutually unbiased bases
(MUBs) in quantum information theory and harmonic frames for the analysis of signals …

Many problems in areas such as compressive sensing and coding theory seek to design a
set of equal-norm vectors with large angular separation. This idea is essentially equivalent …

Equiangular tight frames (ETFs) and biangular tight frames (BTFs)–sets of unit vectors with
basis-like properties whose pairwise absolute inner products admit exactly one or two …

Frame theory has been a popular subject in the design of structured signals and codes in
recent years, with applications ranging from the design of measurement matrices in …

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Many “highly symmetric” configurations of vectors in C d, such as the vertices of the platonic
solids and the regular complex polytopes, are equal-norm tight frames by virtue of being the …