Title :
A directional, shift insensitive, low-redundancy, wavelet transform
Author :
Fernandes, Felix C A ; van Spaendonck, Rutger L. ; Burrus, C. Sidney
Author_Institution :
Dept. of Electr. & Comput. Eng., Rice Univ., Houston, TX, USA
fDate :
6/23/1905 12:00:00 AM
Abstract :
Shift sensitivity and poor directionality, two major disadvantages of the discrete wavelet transform, have previously been circumvented either by using highly redundant, non-separable wavelet transforms or by using restrictive designs to obtain a pair of wavelet trees with a transform-domain redundancy of 4.0 in 2D. We demonstrate that excellent shift-invariance properties and directional selectivity may be obtained with a transform-domain redundancy of only 2.67 in 2D. We achieve this by projecting the wavelet coefficients from Selesnick´s (see Wavelet Applications VII, Proceedings of SPIE, 2000) shift-insensitive, double-density wavelet transform so as to separate approximately the positive and negative frequencies, thereby increasing directionality. Subsequent decimation and a novel inverse projection maintain the low redundancy while ensuring perfect reconstruction. Although our transform generates complex-valued coefficients that provide valuable phase information, it may be implemented with a fast algorithm that uses only real arithmetic. To demonstrate the efficacy of our new transform, we show that it achieves state-of-the-art performance in a seismic image-processing application
Keywords :
channel bank filters; discrete wavelet transforms; filtering theory; geophysical signal processing; image processing; seismology; signal reconstruction; analysis filter bank; complex-valued coefficients; decimation; directional selectivity; directional wavelet transform; discrete wavelet transform; double-density wavelet transform; image-processing applications; inverse projection; low-redundancy wavelet transform; negative frequencies; nonseparable wavelet transforms; perfect reconstruction; phase information; positive frequencies; real arithmetic; redundant wavelet transforms; seismic image-processing; shift insensitive wavelet transform; synthesis filter bank; transform-domain redundancy; wavelet coefficients; wavelet trees; Arithmetic; Discrete transforms; Discrete wavelet transforms; Filter bank; Frequency; Geoscience; Hydrogen; Image reconstruction; Wavelet coefficients; Wavelet transforms;
Conference_Titel :
Image Processing, 2001. Proceedings. 2001 International Conference on
Conference_Location :
Thessaloniki
Print_ISBN :
0-7803-6725-1
DOI :
10.1109/ICIP.2001.959121