Spectrally Two–Uniform Frames For Erasures
Keywords
Connected frames; Erasures; Frames; K -independent sets; Redundancy distribution; Spectrally optimal dual frames
Abstract
We continue to work on the problem of characterizing erasure-optimal frames when spectral radius is used as a measurement of the error operator. Spectrally optimal (N,n) -frames for one erasures are the ones that the minimal spectral error n/N can be achieved. This class of frames was completely characterized in [28] in terms of the connectivity property and the redundancy distributions of the involved frames. We show that the best spectral error for the two erasures is always greater than or equal to [Formula Presented]. We characterize all the frames such that the above lower bound can be achieved. Different characterizations are also obtained for the case that when N = n+1 or n+2. We show that in these special cases, spectrally 2-erasure optimal frames are related to the n-independence property of frames.
Publication Date
6-1-2015
Publication Title
Operators and Matrices
Volume
9
Issue
2
Number of Pages
383-399
Document Type
Article
Personal Identifier
scopus
DOI Link
https://doi.org/10.7153/oam-09-23
Copyright Status
Unknown
Socpus ID
84929168839 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/84929168839
STARS Citation
Pehlivan, Saliha; Han, Deguang; and Mohapatra, Ram, "Spectrally Two–Uniform Frames For Erasures" (2015). Scopus Export 2015-2019. 796.
https://stars.library.ucf.edu/scopus2015/796