A New Framework for Complex Wavelet Transforms

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Title: A New Framework for Complex Wavelet Transforms
Author: Fernandes, Felix; van Spaendonck, Rutger; Burrus, C. Sidney
Type: Journal Paper
Keywords: complex wavelet transforms directionality shift invariance phase non-redundant
Citation: F. Fernandes, R. van Spaendonck and C. S. Burrus, "A New Framework for Complex Wavelet Transforms," IEEE Transactions on Signal Processing, 2003.
Abstract: 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.
Date Published: 2003-06-20

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  • DSP Publications [508 items]
    Publications by Rice Faculty and graduate students in digital signal processing.