The Finer Directional Wavelet Transform

Abstract

Directional information is an important and unique feature of multidimensional signals. As a result of a separable extension from 1D bases, the multidimensional wavelet transform has very limited directionality. Furthermore, different directions are mixed in certain wavelet subbands. In this paper, we propose a new transform that fixes this frequency mixing problem by using a simple "add-on" to the wavelet transform. In the 2D case, it provides one lowpass subband and six directional highpass subbands at each scale. Just like the wavelet transform, the proposed transform is nonredundant, and can be easily extended to higher dimensions. Though nonseparable in essence, the proposed transform has an efficient implementation based on 1D operations only.