13 citations · 77 across the 21 of their papers we have counts for
4 papers · 1 filter
Fusion Frame Homotopy and Tightening Fusion Frames by Gradient Descent
Tom Needham, Clayton Shonkwiler
Finite frames, or spanning sets for finite-dimensional Hilbert spaces, are a ubiquitous tool in signal processing. There has been much recent work on understanding the global struc…
Toric Symplectic Geometry and Full Spark Frames
Tom Needham, Clayton Shonkwiler
The collection of complex matrices with prescribed column norms and prescribed (nonzero) singular values forms a compact algebraic variety, which we refer to as a fram…
Admissibility and Frame Homotopy for Quaternionic Frames
Tom Needham, Clayton Shonkwiler
We consider the following questions: when do there exist quaternionic frames with given frame spectrum and given frame vector norms? When such frames exist, is it always possible t…
Symplectic Geometry and Connectivity of Spaces of Frames
Tom Needham, Clayton Shonkwiler
Frames provide redundant, stable representations of data which have important applications in signal processing. We introduce a connection between symplectic geometry and frame the…