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A New Family of Complex Rotation-Covariant Multiresolution Bases in 2D

B. Forster, T. Blu, M. Unser

Proceedings of the SPIE Conference on Mathematical Imaging: Wavelet Applications in Signal and Image Processing X, San Diego CA, USA, August 4-8, 2003, vol. 5207, part I, pp. 475-479.



We present complex rotation-covariant multiresolution families aimed for image analysis. Since they are complex-valued functions, they provide the important phase information, which is missing in the discrete wavelet transform with real wavelets.

Our basis elements have nice properties in Hilbert space such as smoothness of fractional order α ∈ R+. The corresponding filters allow a FFT-based implementation and thus provide a fast algorithm for the wavelet transform.


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