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摘要: 小波基的冗余可导致鲁棒性,冗余使得低精度下获得的小波系数能在相对高的精度下重建原始信号.本文详细讨论在连续和离散两种情况下小波变换系数在二维时间-尺度空间中的冗余性问题,其中包括:1)小波基自身冗余性的分析,2)信号本身冗余性的分析,3)变换系数冗余性同小波基冗余性之间的关系,4)变换系数冗余性同信号冗余性之间的关系.最后给出体现变换系数冗余性、小波基冗余性以及信号自身冗余性这三者之间关系的统一表达式.Abstract: Redundancy of wavelet bases leads to robustness that the wavelet transform coefficient obtained in low accuracy can be used to reconstruct the original signal with comparative high accuracy. Redundancy of continuous and discreet wavelet coefficients in time-scale space is discussed in this paper, including: 1) redundancy analysis of wavelet bases, 2) redundancy analysis of signal, 3) relation between wavelet coefficient redundancy and wavelet base redundancy, 4) relation between coefficient redundancy and signal redundancy. Expression to represent the relation between coefficient redundancy, frame redundancy, and signal redundancy is proposed at last.
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Key words:
- Wavelet bases /
- sampling theory /
- wavelet reproducing kernel function /
- complete reconstruction /
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