Non-separable wavelets

Non-separable wavelets are multi-dimensional wavelets that are not implemented using one-dimensional operations. They are studied since 1992. In contrast to separable wavelets, the non-separable wavelets have several advantages. For example, the non-separable filters imply more parameters in design. This consequently leads to better filters.

ExamplesEdit

  • Red-black wavelets[1]
  • Contourlets[2]
  • Shearlets[3]
  • Directionlets[4]
  • Steerable pyramids[5]
  • Non-separable schemes for tensor-product wavelets[6]

ReferencesEdit

  1. G. Uytterhoeven and A. Bultheel, "The Red-Black Wavelet Transform," in IEEE Signal Processing Symposium, pp. 191–194, 1998.
  2. M. N. Do and M. Vetterli, "The contourlet transform: an efficient directional multiresolution image representation," IEEE Transactions Image on Processing, vol. 14, no. 12, pp. 2091–2106, Dec. 2005.
  3. G. Kutyniok and D. Labate, "Shearlets: Multiscale Analysis for Multivariate Data," 2012.
  4. V. Velisavljevic, B. Beferull-Lozano, M. Vetterli and P. L. Dragotti, "Directionlets: anisotropic multi-directional representation with separable filtering," IEEE Trans. on Image Proc., Jul. 2006.
  5. E. P. Simoncelli and W. T. Freeman, "The Steerable Pyramid: A Flexible Architecture for Multi-Scale Derivative Computation," in IEEE Second Int'l Conf on Image Processing. Oct. 1995.
  6. D. Barina, M. Kula and P. Zemcik, "Parallel wavelet schemes for images," J Real-Time Image Proc, vol. 16, no. 5, pp. 1365–1381, Oct. 2019.