Frequency-domain analysis of discrete wavelet transform coefficients and their adaptive shrinkage for anti-aliasing

2013 ◽  
Author(s):  
Eunjung Chae ◽  
Eunsung Lee ◽  
Wonseok Kang ◽  
Younghoon Lim ◽  
Junghoon Jung ◽  
...  
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Frequency Domain ◽  
Domain Analysis ◽  
Frequency Domain Analysis ◽  
Discrete Wavelet ◽  
Transform Coefficients ◽  
Adaptive Shrinkage

PERFECT-TRANSLATION-INVARIANT CUSTOMIZABLE COMPLEX DISCRETE WAVELET TRANSFORM

2013 ◽  
Vol 11 (04) ◽  
pp. 1360003 ◽  
Author(s):  
HIROSHI TODA ◽  
ZHONG ZHANG ◽  
TAKASHI IMAMURA
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Frequency Domain ◽  
Wavelet Transforms ◽  
Wavelet Packet ◽  
Variable Density ◽  
Discrete Wavelet ◽  
Translation Invariance ◽  
Translation Invariant ◽  
High Degree

The theorems, giving the condition of perfect translation invariance for discrete wavelet transforms, have already been proven. Based on these theorems, the dual-tree complex discrete wavelet transform, the 2-dimensional discrete wavelet transform, the complex wavelet packet transform, the variable-density complex discrete wavelet transform and the real-valued discrete wavelet transform, having perfect translation invariance, were proposed. However, their customizability of wavelets in the frequency domain is limited. In this paper, also based on these theorems, a new type of complex discrete wavelet transform is proposed, which achieves perfect translation invariance with high degree of customizability of wavelets in the frequency domain.

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