Non-separable wavelets

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

Examples

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

References

↑ G. Uytterhoeven and A. Bultheel, "The Red-Black Wavelet Transform," in IEEE Signal Processing Symposium, pp. 191–194, 1998.
↑ 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.
↑ G. Kutyniok and D. Labate, "Shearlets: Multiscale Analysis for Multivariate Data," 2012.
↑ 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.
↑ 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.
↑ 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.

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[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.

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