Complex wavelets for shift invariant analysis and filtering of signals.

*(English)*Zbl 0990.94005The author uses a dual tree of wavelet filters to have limited redundancy and allow approximate shift invariance and directionally selective filters while preserving perfect reconstruction and computational efficiency with well-balanced frequency responses. This discrete wavelet transform generates complex coefficients whose real and imaginary parts are obtained by means of the dual tree. Two variants of this new transform, based on odd/even and quarter-sample shift (Q-shift) filters, are discussed. Generalization to images and other multi-dimensional signals is briefly described and a range of applications is listed.

Reviewer: Rémi Vaillancourt (Ottawa)

##### MSC:

94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |

93E11 | Filtering in stochastic control theory |

65T60 | Numerical methods for wavelets |

##### Keywords:

complex wavelet; dual tree; shift invariance; limited redundancy; signal filtering; multi-dimensional signals##### Software:

DT-CWT
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\textit{N. Kingsbury}, Appl. Comput. Harmon. Anal. 10, No. 3, 234--253 (2001; Zbl 0990.94005)

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##### References:

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