Generalized frame multiresolution analysis of abstract Hilbert spaces and their applications

Manos Papadakis

doi:10.1117/12.408601

4 December 2000 Generalized frame multiresolution analysis of abstract Hilbert spaces and their applications

Manos Papadakis

Proceedings Volume 4119, Wavelet Applications in Signal and Image Processing VIII; (2000) https://doi.org/10.1117/12.408601
Event: International Symposium on Optical Science and Technology, 2000, San Diego, CA, United States

Abstract

We define a very generic class of multiresolution analysis of abstract Hilbert spaces. Their core subspaces have a frame produced by the action of an abelian unitary group on a perhaps infinite subset of the core subspace, which we call frame multi scaling vector set. We characterize the associated frame multi wavelet vector sets by generalizing the concept of the low and high pass filters and the Quadrature Mirror filter condition. We include an extensive overview of related work of other and we conclude with some examples.

Citation Download Citation

Manos Papadakis "Generalized frame multiresolution analysis of abstract Hilbert spaces and their applications", Proc. SPIE 4119, Wavelet Applications in Signal and Image Processing VIII, (4 December 2000); https://doi.org/10.1117/12.408601

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