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13 papers · 1 filter
On the value of the fifth maximal projection constant
Beata Derȩgowska, Matthew Fickus, Simon Foucart +1
Let denote the maximal absolute projection constant over real -dimensional subspaces. This quantity is extremely hard to determine exactly, as testified by the fact that…
Detailing the equivalence between real equiangular tight frames and certain strongly regular graphs
Matthew Fickus, Cody E. Watson
An equiangular tight frame (ETF) is a set of unit vectors whose coherence achieves the Welch bound, and so is as incoherent as possible. They arise in numerous applications. It is…
Tables of the existence of equiangular tight frames
Matthew Fickus, Dustin G. Mixon
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).…
Phase retrieval from very few measurements
Matthew Fickus, Dustin G. Mixon, Aaron A. Nelson +1
In many applications, signals are measured according to a linear process, but the phases of these measurements are often unreliable or not available. To reconstruct the signal, one…
Saving phase: Injectivity and stability for phase retrieval
Afonso S. Bandeira, Jameson Cahill, Dustin G. Mixon +1
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:…
Group-theoretic constructions of erasure-robust frames
Matthew Fickus, John Jasper, Dustin G. Mixon +1
In the field of compressed sensing, a key problem remains open: to explicitly construct matrices with the restricted isometry property (RIP) whose performance rivals those generate…