A directional, shift insensitive, low-redundancy, wavelet transform

Shift variance and poor directional selectivity, 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. In this paper, we demonstrate that excellent shift-invariance properties and directional selectivity may be obtained with a transformdomain redundancy of only 2.67 in 2D. We achieve this by projecting the wavelet coefficients from Selesnick's almost shiftinvariant, 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 allowing processing capabilities that are impossible with real-valued coefficients, ...

• Type: Conference
• Year: 2001
• Where: ICIP
• Authors: Rutger L. van Spaendonck, Felix C. A. Fernandes, S. Sidney Burrus
• Keywords: Discrete Wavelet Transform, Double-density Wavelet Transform, ICIP 2001, Image Processing, Wavelet Coefficients