126 citations · 348 across the 94 of their papers we have counts for
7 papers · 1 filter
Non-orthogonal fusion frames and the sparsity of fusion frame operators
Jameson Cahill, Peter Casazza, Shidong Li
Fusion frames have become a major tool in the implementation of distributed systems. The effectiveness of fusion frame applications in distributed systems is reflected in the effic…
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…
Optimally Sparse Frames
Peter G. Casazza, Andreas Heinecke, Felix Krahmer +1
Frames have established themselves as a means to derive redundant, yet stable decompositions of a signal for analysis or transmission, while also promoting sparse expansions. Howev…
A quantitative notion of redundancy for infinite frames
Jameson Cahill, Peter G. Casazza, Andreas Heinecke
Bodmann, Casazza and Kutyniok introduced a quantitative notion of redundancy for finite frames - which they called {\em upper and lower redundancies} - that match better with an in…
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…
Concrete constructions of non-pavable projections
Peter G. Casazza, Matt Fickus, Dustin Mixon +1
It is known that the paving conjecture fails for 2-paving projections with constant diagonal 1/2. But the proofs of this fact are existence proofs. We will give concrete examples o…
Spanning and independence properties of frame partitions
Bernhard G. Bodmann, Peter G. Casazza, Vern I. Paulsen +1
We answer a number of open problems in frame theory concerning the decomposition of frames into linearly independent and/or spanning sets. We prove that in finite dimensional Hilbe…