Related papers: Construction of k-angle tight frames
This paper supplies additions to our paper in Linear Algebra Appl. 510 (2016) 395--420 on integral spans of tight frames in Euclidean spaces. In that previous paper, we considered the case of an equiangular tight frame (ETF), proving that…
Neural collapse is a phenomenon observed during the terminal phase of neural network training, characterized by the convergence of network activations, class means, and linear classifier weights to a simplex equiangular tight frame (ETF), a…
An equi-isoclinic tight fusion frame (EITFF) is a type of Grassmannian code, being a sequence of subspaces of a finite-dimensional Hilbert space of a given dimension with the property that the smallest spectral distance between any pair of…
Given a channel with additive noise and adversarial erasures, the task is to design a frame that allows for stable signal reconstruction from transmitted frame coefficients. To meet these specifications, we introduce numerically…
Over-complete systems of vectors, or in short, frames, play the role of analog codes in many areas of communication and signal processing. To name a few, spreading sequences for code-division multiple access (CDMA), over-complete…
We introduce a general technique to construct tight fusion frames with prescribed symmetries. Applying this technique with a prescription for "all the symmetries", we construct a new family of equi-isoclinic tight fusion frames (EITFFs),…
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 characterisations of projective and unitary equivalence.…
Analog coding is a low-complexity method to combat erasures, based on linear redundancy in the signal space domain. Previous work examined "band-limited discrete Fourier transform (DFT)" codes for Gaussian channels with erasures or…
Finite frames, or spanning sets for finite-dimensional Hilbert spaces, are a ubiquitous tool in signal processing. There has been much recent work on understanding the global structure of collections of finite frames with prescribed…
We show that there does not exist a complex $d\times n$ equiangular tight frame with \[ d^2-d+1<n<d^2. \] The proof, which originated from an internal model at OpenAI, mimics the relationship between real equiangular tight frames and…
Spectral tetris is a fexible and elementary method to construct unit norm frames with a given frame operator, having all of its eigenvalues greater than or equal to two. One important application of spectral tetris is the construction of…
In this paper, we show how one may (efficiently) construct two types of extremal combinatorial objects whose existence was previously conjectural. (*) Panchromatic Graphs: For fixed integer k, a k-panchromatic graph is, roughly speaking, a…
Let $q\geq 2$ be an integer, and $\Bbb F_q^d$, $d\geq 1$, be the vector space over the cyclic space $\Bbb F_q$. The purpose of this paper is two-fold. First, we obtain sufficient conditions on $E \subset \Bbb F_q^d$ such that the inverse…
We introduce probabilistic frames to study finite frames whose elements are chosen at random. While finite tight frames generalize orthonormal bases by allowing redundancy, independent, uniformly distributed points on the sphere…
Configurations of subspaces like equichordal and equiisoclinic tight fusion frames, which are in some sense optimally spread apart and which also have reconstruction properties emulating those of orthonormal bases, are useful in various…
We consider estimating a random vector from its noisy projections onto low dimensional subspaces constituting a fusion frame. A fusion frame is a collection of subspaces, for which the sum of the projection operators onto the subspaces is…
Recently, the application of advanced machine learning methods for asset management has become one of the most intriguing topics. Unfortunately, the application of these methods, such as deep neural networks, is difficult due to the data…
This paper presents a method of constructing Parseval frames from any collection of complex envelopes. The resulting Enveloped Sinusoid Parseval (ESP) frames can represent a wide variety of signal types as specified by their physical…
We propose Equiangular Basis Vectors (EBVs) for classification tasks. In deep neural networks, models usually end with a k-way fully connected layer with softmax to handle different classification tasks. The learning objective of these…
This paper introduces a design method for densergraph-frequency graph Fourier frames (DGFFs) to enhance graph signal processing and analysis. The graph Fourier transform (GFT) enables us to analyze graph signals in the graph spectral domain…