Non-separable wavelet explained
Non-separable wavelets are multi-dimensional wavelets that are not directly implemented as tensor products of wavelets on some lower-dimensional space.They have been studied since 1992.[1] They offer a few important advantages. Notably, using non-separable filters leads to more parameters in design, and consequently better filters.[2] The main difference, when compared to the one-dimensional wavelets, is that multi-dimensional sampling requires the use of lattices (e.g., the quincunx lattice).The wavelet filters themselves can be separable or non-separable regardless of the sampling lattice.Thus, in some cases, the non-separable wavelets can be implemented in a separable fashion.Unlike separable wavelet, the non-separable wavelets are capable of detecting structures that are not only horizontal, vertical or diagonal (show less anisotropy).
Examples
References
- J. Kovacevic and M. Vetterli, "Nonseparable multidimensional perfect reconstruction filter banks and wavelet bases for Rn," IEEE Trans. Inf. Theory, vol. 38, no. 2, pp. 533–555, Mar. 1992.
- J. Kovacevic and M. Vetterli, "Nonseparable two- and three-dimensional wavelets," IEEE Transactions on Signal Processing, vol. 43, no. 5, pp. 1269–1273, May 1995.
- 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 on Image Processing, vol. 14, no. 12, pp. 2091–2106, Dec. 2005.
- [Gitta Kutyniok|G. Kutyniok]
- 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.
- [Eero Simoncelli|E. P. Simoncelli]
- 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.
