Linearly connected sequences and spectrally optimal dual frames for erasures
Abbreviated Journal Title
J. Funct. Anal.
Frames; Erasures; Spectrally optimal dual frames; Connected frames; Redundancy distribution; k-independent sets; EQUIANGULAR TIGHT FRAMES; SEIDEL MATRICES; PARSEVAL FRAMES; REPRESENTATIONS; COMMUNICATION; Mathematics
In the case that a frame is prescribed for applications and erasures occur in the process of data transmissions, we examine optimal dual frames for the recovery from single erasures. In contrast to earlier papers, we consider the spectral radius of the error operator instead of its operator norm as a measure of optimality. This notion of optimality is natural when the Neumann series is used to recover the original data in an iterative manner. We obtain a complete characterization of spectrally one-erasure optimal dual frames in terms of the redundancy distribution of the prescribed frame. Our characterization relies on the connection. between erasure optimal frames and the linear connectivity property of the frame. We prove that the linear connectivity property is equivalent to the intersection dependent property, and is also closely related to the well-known concept of a k-independent set. Additionally, we also establish several necessary and sufficient conditions for the existence of an alternate dual frame to make the iterative reconstruction work. (C) 2013 Elsevier Inc. All rights reserved.
Journal of Functional Analysis
"Linearly connected sequences and spectrally optimal dual frames for erasures" (2013). Faculty Bibliography 2010s. 4522.