Designing thin wavelet filters

In this paper we design thin n-D wavelet filters. Our wavelet filters are thin in the sense that each filter is essentially a 1-D filter, which is supported on a straight line. We first use the coset sum, a recently developed alternative to the tensor product, in order to obtain thin n-D wavelet filters that can capture directional information in 2 ⁿ - 1 different directions. Furthermore the choice of directions is quite flexible, and it can be made so that there is no strong directional bias along lines parallel to the coordinate direction. One limitation of thin n-D wavelet filters constructed by the coset sum method is that they can capture only 2 ⁿ - 1 directions. In order to overcome this limitation we discuss how to generalize the coset sum method so that thin n-D Haar wavelet filters with more than 2 ⁿ - 1 directions can be obtained.