Discrete directional wavelet bases for image compression

The application of the wavelet transform in image processing is most frequently based on a separable construction. Lines and columns in an image are treated independently and the basis functions are simply products of the corresponding one dimensional functions. Such method keeps simplicity in design and computation, but is not capable of capturing properly all the properties of an image. In this paper, a new truly separable discrete multi-directional transform is proposed with a subsampling method based on lattice theory. Alternatively, the subsampling can be omitted and this leads to a multi-directional frame. This transform can be applied in many areas like denoising, non-linear approximation and compression. The results on non-linear approximation and denoising show very interesting gains compared to the standard two-dimensional analysis.