Directional dyadic wavelet transforms: design and algorithms

We propose a simple and efficient technique for designing translation invariant dyadic wavelet transforms (DWTs) in two dimensions. Our technique relies on an extension of the work of Duval-Destin et al. where dyadic decompositions are constructed starting from the continuous wavelet transform. The main advantage of this framework is that it allows for a lot of freedom in designing two-dimensional (2-D) dyadic wavelets. We use this property to construct directional wavelets, whose orientation filtering capabilities are very important in image processing. We address the efficient implementation of these decompositions by constructing approximate QMFs through an L(2) optimization. We also propose and study an efficient implementation in the Fourier domain for dealing with large filters.