B-spline quincunx wavelet transform and implementation in Fourier domain
Frédéric Nicolier, Olivier Laligant, Frédéric Truchetet · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1998
In this paper an efficient method is presented to cope with the need of phase linear filters in orthonormal wavelet transform for image processing. Phase linear filtering can be obtained in two dimensions by using Cohen/Daubechies biorthogonal wavelets. But as orthogonal analysis is preferable, a new method to construct orthonormal bidimensional wavelet base in the quincunx scheme is proposed. These filters are designed by applying the McClellan Transform on 1D B-spline filters in order to get 2D orthonormal quincunx non-separable ones. This method takes advantage of the orthogonality of the analysis and of the quincunx scheme, indeed these filters lead to only one approximation image and only one detail image. The interscale resolution given by this analysis is twice more accurate than in the case of a separable analysis and the wavelet functions have better isotropic and frequency properties than those previously proposed by Feauveau.