Discrete directional wavelet bases and frames: analysis and applications

Pier Luigi Dragotti; Vladan Velisavljevic; Martin Vetterli; Baltasar Beferull-Lozano

doi:10.1117/12.506741

13 November 2003 Discrete directional wavelet bases and frames: analysis and applications

Pier Luigi Dragotti, Vladan Velisavljevic, Martin Vetterli, Baltasar Beferull-Lozano

Proceedings Volume 5207, Wavelets: Applications in Signal and Image Processing X; (2003) https://doi.org/10.1117/12.506741
Event: Optical Science and Technology, SPIE's 48th Annual Meeting, 2003, San Diego, California, United States

Abstract

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.

Citation Download Citation

Pier Luigi Dragotti, Vladan Velisavljevic, Martin Vetterli, and Baltasar Beferull-Lozano "Discrete directional wavelet bases and frames: analysis and applications", Proc. SPIE 5207, Wavelets: Applications in Signal and Image Processing X, (13 November 2003); https://doi.org/10.1117/12.506741

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