Study on Properties of Directional Filter Banks in the Dual Tree Scheme

The dual tree is an efficient scheme to improve shift invariance and achieve phase information of a signal, and the directional filter banks (DFBs) is a widespread used tool to achieve greater directional selectivity for two dimension (2D) images. However, the dual tree based on separable filter banks can only discriminate six-direction information in 2D and the DFBs can not provide shift in-variance and phase information. The dual tree scheme based on the nonseparable DFBs may easily improve shift invariance, directional selectivity and provide phase information. This paper presents new properties of the DFBs employed in the dual tree scheme and deduces three new classes of nonseparable filters. The computation requirements of the scheme can be reduced by arranging the filters according to these properties. Besides, an appropriate definition of 2D analytic signal is employed to simplify the process of designing these new filters derived from nonseparable prototype filters.