Quantized frame expansions with erasures

被引:332
作者
Goyal, VK
Kovacevic, J
Kelner, JA
机构
[1] Bell Labs, Lucent Technol, Math Commun Res, Murray Hill, NJ 07974 USA
[2] Harvard Univ, Cambridge, MA 02138 USA
关键词
D O I
10.1006/acha.2000.0340
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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. (C) 2001 Academic Press.
引用
收藏
页码:203 / 233
页数:31
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