Recent advances in convex optimization have led to new strides in the phase retrieval problem
over finite-dimensional vector spaces. However, certain fundamental questions remain: …

This paper is concerned with an important matrix condition in compressed sensing known
as the restricted isometry property (RIP). We demonstrate that testing whether a matrix …

We provide a new method for constructing equiangular tight frames (ETFs). The construction
is valid in both the real and complex settings, and shows that many of the few previously-…

Finite frame theory has a number of real-world applications. In applications like sparse
signal processing, data transmission with robustness to erasures, and reconstruction without …

In many areas of imaging science, it is difficult to measure the phase of linear measurements.
As such, one often wishes to reconstruct a signal from intensity measurements, that is, …

We consider the classical 1D phase retrieval problem. In order to overcome the difficulties
associated with phase retrieval from measurements of the Fourier magnitude, we treat …

The restricted isometry property (RIP) is a well-known matrix condition that provides state-of-the-art
reconstruction guarantees for compressed sensing. While random matrices are …

A Grassmannian frame is a collection of unit vectors which are optimally incoherent. To date,
the vast majority of explicit Grassmannian frames are equiangular tight frames (ETFs). This …

Background Terahertz (THz) radiation sources are increasingly being used in military,
defense, and medical applications. However, the biological effects associated with this type of …

Neural collapse is an emergent phenomenon in deep learning that was recently discovered
by Papyan, Han and Donoho. We propose a simple "unconstrained features model" in …