Directional wavelet transforms and frames

Abstract

The application of the wavelet transform in image processing is most frequently based on a separable transform. Lines and columns in an image are treated independently and the basis functions are simply products of corresponding one-dimensional functions. Such a method keeps simplicity in design and computation. A new two-dimensional approach is proposed, which retains the simplicity of separable processing, but allows more directionalities. The method can be applied in many areas like denoising, nonlinear approximation and compression. The results on nonlinear approximation and denoising show interesting gains compared to the standard two-dimensional analysis.