A new framework for complex wavelet transforms

被引:90
作者
Fernandes, FCA [1 ]
van Spaendonck, RLC
Burrus, CS
机构
[1] Texas Instruments Inc, DSPS Res & Dev Ctr, Dallas, TX 75025 USA
[2] Delft Univ Technol, Dept Earth Sci, Delft, Netherlands
[3] Rice Univ, Dept Elect & Comp Engn, Houston, TX 77001 USA
关键词
complex wavelet transforms; directional redundancy; Hardy space; Hilbert transform; shift invariant; shift sensitivity;
D O I
10.1109/TSP.2003.812841
中图分类号
TM [电工技术]; TN [电子技术、通信技术];
学科分类号
0808 ; 0809 ;
摘要
Although the discrete wavelet transform (DWT) is a powerful tool for signal and image processing, it has three serious disadvantages: shift sensitivity, poor directionality, and lack of phase information. To overcome these disadvantages, we introduce two-stage mapping-based complex wavelet transforms that consist of a mapping onto a complex function space followed by a DWT of the complex mapping. Unlike other popular transforms that also mitigate DWT shortcomings, the decoupled implementation of our transforms has two important advantages. First, the controllable redundancy of the mapping stage offers a balance between degree of shift sensitivity and transform redundancy. This allows us to create a directional, non-redundant, complex wavelet transform with potential benefits for image coding systems. To the best of our knowledge, no other complex wavelet transform is simultaneously directional and non-redundant. The second advantage of our approach is the flexibility to use any DWT in the transform implementation. As an example we can exploit this flexibility to-create the complex double-density DWT (CDDWT): a shift-insensitive, directional, complex wavelet transform with a low redundancy of (3(m) - 1/2(m) - 1) in m dimensions. To the best of our knowledge, no other transform achieves all these properties at a lower redundancy.
引用
收藏
页码:1825 / 1837
页数:13
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