Equal-norm tight frames with erasures
type: Item
instance of: scholarly article
title: Equal-norm tight frames with erasures
zbMATH Open document ID: 1035.42029
DOI: 10.1023/A:1021349819855
author: Peter G. Casazza
author: Jelena Kovačević
published in: Advances in Computational Mathematics
publication date: 2003-04-10T00:00:00Z
review text: Given a Hilbert space \(H\), a collection \(\{e_i: i \in I \} \subset H\) is called a frame if there exist constants \(A, B>0\) such that for all \(f\in H\): \[ A \| f\| ^2 \leq \sum_{i \in I} | \langle f, e_i \rangle | ^2 \leq B \| f\| ^2. \] When \(A=B\) we say that the frame is tight. When all elements \(e_i\) have the same norm, we say the frame is equal-norm, and when this norm is 1 we say the frame is normalized. The paper under review studies equal-norm tight frames in spaces \(R^d\) and \(C^d\), equipped with the usual Euclidean inner product. Typical examples of such frames are harmonic frames, which consist of coordinates of the discrete Fourier transform. The authors show that all equal-norm tight frames generated by one or two unitary operators on \(R^d\) (resp., \(C^d\)) are generalized harmonic frames. The last section of the paper is devoted to the study of frames that remain frames after deletion (erasure) of a finite number of its elements. Such frames are called robust to erasures, and harmonic frames have this property. Characterization of frames robust to \(k\) erasures is given.
reviewed by: Wojciech Czaja
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 1896710
zbMATH Keywords: equal-norm frames
zbMATH Keywords: tight frames
zbMATH Keywords: harmonic frames
zbMATH Keywords: erasures
MaRDI profile type: Publication
full work available at URL: a:1021349819855
OpenAlex ID: W1571821595
description: scientific article; zbMATH DE number 1896710