4 papers · 1 filter
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…
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…
The Bourgain-Tzafriri conjecture and concrete constructions of non-pavable projections
Peter G. Casazza, Matthew Fickus, Dustin G. Mixon +1
It is known that the Kadison-Singer Problem (KS) and the Paving Conjecture (PC) are equivalent to the Bourgain-Tzafriri Conjecture (BT). Also, it is known that (PC) fails for -p…