26 citations
6 papers · 1 filter
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…
The road to deterministic matrices with the restricted isometry property
Afonso S. Bandeira, Matthew Fickus, Dustin G. Mixon +1
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 k…
Optimal frames and Newton's method
Matthew Fickus, Dustin G. Mixon
Given a parametrized family of finite frames, we consider the optimization problem of finding the member of this family whose coefficient space most closely contains a given data v…
Constructing all self-adjoint matrices with prescribed spectrum and diagonal
Matthew Fickus, Dustin G. Mixon, Miriam J. Poteet +1
The Schur-Horn Theorem states that there exists a self-adjoint matrix with a given spectrum and diagonal if and only if the spectrum majorizes the diagonal. Though the original pro…
Steiner equiangular tight frames
Matthew Fickus, Dustin G. Mixon, Janet C. Tremain
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…
Auto-tuning unit norm frames
Peter G. Casazza, Matthew Fickus, Dustin G. Mixon
Finite unit norm tight frames provide Parseval-like decompositions of vectors in terms of redundant components of equal weight. They are known to be exceptionally robust against ad…