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Ondelettes régulières: application à la compression d'images fixes

Abstract : This thesis, started at the end of 1989, is devoted to the study of the effect of new mathematical properties brought by wavelet theory on subband coding, for still image compression problems. Using a theoretical analysis of discrete-time multiresolution decomposition, it is shown that, within our framework, the practical novelty of wavelets reduces to the {\em regularity\/}property of octave-band filter banks used in subband coding schemes. Then, several tools are derived, which make a systematic study of regularity possible, for applications such as image compression. A mathematical study of the regularity property is investigated,in which optimal regularity estimation algorithms are derived. Several filter bank design algorithms are then proposed. They allow one to balance regularity against other filter properties (orthogonality, linear phase response, frequency selectivity, etc.) which are generally believed to be relevant for image coding. Fast algorithms are also derived, for which substancial reduction of computational load required by octave-band filter banks is possible. Finally, an experimental study of filter properties is carried out, for a simple still image compression scheme, in which the wavelet transform is separable. In this restricted framework, the potential interest of regularity is emphasized, in competition with other criteria such as frequency selectivity and linear phase.
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Submitted on : Friday, July 1, 2005 - 8:00:00 AM
Last modification on : Monday, October 19, 2020 - 9:20:01 AM
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  • HAL Id : pastel-00001307, version 1


Olivier Rioul. Ondelettes régulières: application à la compression d'images fixes. domain_other. Télécom ParisTech, 1993. English. ⟨pastel-00001307⟩



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