166 citations · 655 across the 82 of their papers we have counts for
6 papers · 2 filters
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…
Sparse Signal Processing with Frame Theory
Dustin G. Mixon
Many emerging applications involve sparse signals, and their processing is a subject of active research. We desire a large class of sensing matrices which allow the user to discern…
Certifying the restricted isometry property is hard
Afonso S. Bandeira, Edgar Dobriban, Dustin G. Mixon +1
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 satis…
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…
Numerically erasure-robust frames
Matthew Fickus, Dustin G. Mixon
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 mee…