Quantized Frame Expansions with Erasures

Vivek K. Goyal, Jelena Kovacevic, Jonathan A. Kelner

Research output: Contribution to journalArticle

Abstract

Frames have been used to capture significant signal characteristics, provide numerical stability of reconstruction, and enhance resilience to additive noise. This paper places frames in a new setting, where some of the elements are deleted. Since proper subsets of frames are sometimes themselves frames, a quantized frame expansion can be a useful representation even when some transform coefficients are lost in transmission. This yields robustness to losses in packet networks such as the Internet. With a simple model for quantization error, it is shown that a normalized frame minimizes mean-squared error if and only if it is tight. With one coefficient erased, a tight frame is again optimal among normalized frames, both in average and worst-case scenarios. For more erasures, a general analysis indicates some optimal designs. Being left with a tight frame after erasures minimizes distortion, but considering also the transmission rate and possible erasure events complicates optimizations greatly.

Original languageEnglish (US)
Pages (from-to)203-233
Number of pages31
JournalApplied and Computational Harmonic Analysis
Volume10
Issue number3
DOIs
StatePublished - May 1 2001

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Additive noise
Packet networks
Convergence of numerical methods
Tight Frame
Internet
Minimise
Proper subset
Resilience
Additive Noise
Numerical Stability
Coefficient
Mean Squared Error
Quantization
Transform
Robustness
If and only if
Scenarios
Optimization
Optimal design
Model

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Quantized Frame Expansions with Erasures. / Goyal, Vivek K.; Kovacevic, Jelena; Kelner, Jonathan A.

In: Applied and Computational Harmonic Analysis, Vol. 10, No. 3, 01.05.2001, p. 203-233.

Research output: Contribution to journalArticle

Goyal, Vivek K. ; Kovacevic, Jelena ; Kelner, Jonathan A. / Quantized Frame Expansions with Erasures. In: Applied and Computational Harmonic Analysis. 2001 ; Vol. 10, No. 3. pp. 203-233.
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