A multiresolution directional filter bank for image applications

We propose a new formulation of directional filter banks (DFBs). By using a non-uniform and non-separable filter bank, a critically sampled multiresolution directional image representation can be obtained efficiently. The resulting DFB yields non-uniform frequency division which is composed of one lowpass channel with a decimation factor of one-fourth and six highpass directional channels with a decimation factor of one-eighth. It overcomes the limited directional selectivity of separable wavelets and the limited resolution of the conventional DFB. The lowpass channel can be used to obtain multiresolution representation by simply re-iterating the same DFB decomposition. On the other hand, the directional subbands can be further refined by simply applying a two-channel DFB at each highpass channel. A simple design method yielding near orthogonal uniform and non-uniform multidimensional filter banks is discussed, and, finally, a numerical experiment is presented to demonstrate the potential of the new image basis.