Discrete directional wavelet bases and frames: analysis and applications
Pier Luigi Dragotti, Vladan Velisavljević, Martin Vetterli, Baltasar Beferull‐Lozano · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2003
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 interesting gains compared to the standard two-dimensional analysis.