Orthonormal bases of compactly supported wavelets
Tóm tắt
We construct orthonormal bases of compactly supported wavelets, with arbitrarily high regularity. The order of regularity increases linearly with the support width. We start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction. The construction then follows from a synthesis of these different approaches.
Từ khóa
Tài liệu tham khảo
Meyer Y. Principe d'incertitude bases hilbertiennes et algèbres d'opérateurs Séminaire Bourbaki 1985‐1986 nr. 662.
Tchamitchian P., 1986, Calcul symbolique sur les opérateurs de Calderón‐Zygmund et bases inconditionnelles de L2(ℝn, C. R. Acad. Sc. Paris. 303, série, 1, 215
Tchamitchian P. Biorthogonalité et théorie des opérateurs to be published in Rev. Mat. Iberoamericana.
Battle G. andFederbush P. Ondelettes and phase cell cluster expansions; a vindication Comm. Math. Phys. 1987.
Kronland‐Martinet R. Morlet J. andGrossmann A. Analysis of sound patterns through wavelet transforms to be published in International Journal on Pattern Analysis and Artificial Intelligence.
Mallat S. A theory for multiresolution signal decomposition: the wavelet transform Preprint GRASP Lab Dept. of Computer and Information Science Univ. of Pennsylvania to be published.
Grossmann A. Wavelet transforms and edge detection to be published in Stochastic Processes in Physics and Engineering (Ph. Blanchard L. Streit and M. Hasewinkel eds.)
1986, Examples, Ann. Inst. H. Poincaré, 45, 293
Paul T., 1985, Functions analytic on the half‐plane as quantum mechanical states, J. Math. Phys., 25
pp.3252–3263.Paul T. Affine coherent states and the radial Schrödinger equation. I. Radial harmonic oscillator and hydrogen atom to be published.
Grossmann A. andKronland R. Private demonstration.
Daubechies I. The wavelet transform time‐frequency localization and signal analysis Preprint AT&T Bell Laboratories; to be published.
Meyer Y. Ondelettes et functions splines Séminaire EDP Ecole Polytechnique Paris France December 1986 .
Lemarié P. G. Ondelettes à localisation exponentielle to be published in Journ. de MaTh. Pures et Appl.
Mallat S. Multiresolution approximation and wavelets.Preprint GRASP Lab. Dept. of Computer and Information Science Univ. of Pennsylvania to be published.
Jaffard S. Lemarié P. G. Mallat S. andMeyer Y. Multiscale analysis unpublished memorandum.
Coifman R., The discrete wavelet transform
Auscher P. Thèse de Doctorat Université de Paris‐Dauphine1988.
Rioul O. private communication.
Meyer Y. Wavelets with compact support Zygmund Lectures (University of Chicago) May 1987 and private communication.
Deslauriers G. andDubuc S. Interpolation dyadique in Fractals; Dimensions non Entières et Applications ed. G. Cherbit Masson (Paris) 1987 pp.44–45. See also other references listed there.
Daubechies I. andLagarias J. Two‐scale difference equations. I. Global regularity of solutions and —. II. Infinite matrix products local regularity and fractals Preprints AT&T Bell Laboratories; to be published.