13 November 2003 A new family of complex rotation-covariant multiresolution bases in 2D
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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 ε R+. The corresponding filters allow a FFT-based implementation and thus provide a fast algorithm for the wavelet transform.
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Brigitte Forster, Thierry Blu, Michael A. Unser, "A new family of complex rotation-covariant multiresolution bases in 2D", Proc. SPIE 5207, Wavelets: Applications in Signal and Image Processing X, (13 November 2003); doi: 10.1117/12.503696; https://doi.org/10.1117/12.503696


Discrete wavelet transforms

Fourier transforms

Image analysis

Wavelet transforms


Image filtering


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