Wavelet representations

2-D Orthogonal wavelets

Picture of the Daubechies' Symmlet with 8 vanishing moments. Note the checkerboard pattern in the center.

2-D Complex wavelets

Below are some pictures of a 2-D complex wavelet, designed using the method of Prof. Ivan Selesnick (the degree of zeros at z=-1 is 3, the degree of fractional delay is 2, hence all filter pairs consist of 10 coefficients).

References

• I. Daubechies, "Ten Lectures on Wavelets," CBMS-NSF Lecture Notes nr. 61, SIAM , 1992.
• N G Kingsbury, "Complex wavelets for shift invariant analysis and filtering of signals,"
  Journal of Applied and Computational Harmonic Analysis, vol 10, no 3, May 2001, pp. 234-253.
• I. W. Selesnick. "The design of approximate Hilbert transform pairs of wavelet bases,"
  IEEE Trans. on Signal Processing, 50(5):1144-1152, May 2002.