Name
Abstract | ||
|---|---|---|
The objective of this paper is to improve the customary definition of redundancy by providing quantitative measures in its place, which we coin upper and lower redundancies, that match better with an intuitive understanding of redundancy for finite frames in a Hilbert space. This motivates a carefully chosen list of desired properties for upper and lower redundancies. The means to achieve these properties is to consider the maximum and minimum of a redundancy function, which is interesting in itself. The redundancy function is defined on the sphere of the Hilbert space and measures the concentration of frame vectors around each point. A complete characterization of functions on the sphere which coincide with a redundancy function for some frame is given. The upper and lower redundancies obtained from this function are shown to satisfy all of the intuitively desirable properties. In addition, the range of values they assume is characterized. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1109/CISS.2010.5464807 | Information Sciences and Systems |
Keywords | Field | DocType |
Hilbert spaces,signal processing,Hilbert space,finite frame redundancy,redundancy function,signal processing,signal transmissions,Erasures,Frames,Linearly Independent Sets,Redundancy,Redundancy Function,Spanning Sets,Sparse Approximation | Hilbert space,Signal processing,Discrete mathematics,Mathematical optimization,Computer science,Sparse approximation,Algorithm,Robustness (computer science),Redundancy (engineering),Redundancy (information theory),Quantization (signal processing) | Conference |
ISBN | Citations | PageRank |
978-1-4244-7417-2 | 0 | 0.34 |
References | Authors | |
1 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Bernhard G. Bodmann | 1 | 0 | 0.68 |
| Peter G. Casazza | 2 | 0 | 0.34 |
| Gitta Kutyniok | 3 | 325 | 34.77 |