An equiangular tight frame (ETF) yields a type of optimal packing lines in Euclidean space. ETFs seem to be rare, and all known infinite families them arise from some combinatorial design. In this paper, we introduce new method for constructing ETFs. We begin by showing that it is sometimes possible construct multiple the same space are “mutually unbiased” way analogous quantum-information-theo...

We introduce a class of finite tight frames called prime tight frames and prove some of their elementary properties. We show that any finite tight frame can be written as a union of prime tight frames. We then characterize all prime harmonic tight frames as well as all prime frames constructed from the spectral tetris method. As a byproduct of this last result, we obtain a characterization of w...

Based on the shearlet transform we present a general construction of continuous tight frames for L(R) from any sufficiently smooth function with anisotropic moments. This includes for example compactly supported systems, piecewise polynomial systems, or both. From the results in [5] it follows that these systems enjoy the same desirable approximation properties for directional data as the bandl...

We combine Steiner systems with Hadamard matrices to produce a new class of equiangular tight frames. This in turn leads to new constructions of strongly regular graphs and distance-regular antipodal covers of the complete graph.

A d × n matrix, n ≥ d, whose columns have equal length and whose rows are orthonormal is constructed. This is equivalent to finding an isometric tight frame of n vectors in R d (or C d), or writing the d × d identity matrix I = d n n i=1 P i , where the P i are rank 1 orthogonal projections. The simple inductive procedure given shows that there are many such isometric tight frames.

In this paper‎, ‎using the discrete Fourier transform in the finite-dimensional Hilbert space C^n‎, ‎a class of nonRieszable equal norm tight frames is introduced ‎and‎ using this class, a bound for Fiechtinger Conjecture is presented. By the Fiechtinger Conjecture that has been proved recently, for given A,C>0 there exists a universal constant delta>0 independent of $n$ such that every C-equal...