Real, Tight Frames with Maximal Robustness to Erasures

12 April 2005

conference paper
Published by Institute of Electrical and Electronics Engineers (IEEE)

p. 63-72
https://doi.org/10.1109/dcc.2005.77

Abstract

Motivated by the use of frames for robust transmission over the Internet, we present a first systematic construction of real tight frames with maximum robustness to erasures. We approach the problem in steps: we first construct maximally robust frames by using polynomial transforms. We then add tightness as an additional property with the help of orthogonal polynomials. Finally, we impose the last requirement of equal norm and construct, to our best knowledge, the first real, tight, equal-norm frames maximally robust to erasures.

Keywords

This publication has 8 references indexed in Scilit:

Frames, graphs and erasures
Linear Algebra and its Applications, 2005
Optimal frames for erasures
Linear Algebra and its Applications, 2004
The Algebraic Approach to the Discrete Cosine and Sine Transforms and Their Fast Algorithms
SIAM Journal on Computing, 2003
Equal-Norm Tight Frames with Erasures
Advances in Computational Mathematics, 2003
Quantized Frame Expansions with Erasures
Applied and Computational Harmonic Analysis, 2001
Continuous and Discrete Wavelet Transforms
SIAM Review, 1989
Asymptotic Properties of Discrete Unitary Transforms
Published by Institute of Electrical and Electronics Engineers (IEEE) ,1979
A class of nonharmonic Fourier series
Transactions of the American Mathematical Society, 1952