Showing papers on "Multiresolution analysis published in 1990"

Resolution of the 1D regularized Burgers equation using a spatial wavelet approximation

Abstract: The Burgers equation with a small viscosity term, initial and periodic boundary conditions is resolved using a spatial approximation constructed from an orthonormal basis of wavelets. The algorithm is directly derived from the notions of multiresolution analysis and tree algorithms. Before the numerical algorithm is described these notions are first recalled. The method uses extensively the localization properties of the wavelets in the physical and Fourier spaces. Moreover, the authors take advantage of the fact that the involved linear operators have constant coefficients. Finally, the algorithm can be considered as a time marching version of the tree algorithm. The most important point is that an adaptive version of the algorithm exists: it allows one to reduce in a significant way the number of degrees of freedom required for a good computation of the solution. Numerical results and description of the different elements of the algorithm are provided in combination with different mathematical comments on the method and some comparison with more classical numerical algorithms.

IFS fractals and the wavelet transform

Abstract: Iterated function systems (IFSs) are capable of effectively describing complex shapes and textures by fractals. The interscale properties of such fractals are analyzed with the aid of the wavelet transform and general multiresolution analysis. The result is a formulation for homogeneous IFSs in general scale space which leads to a direct solution of the inverse problem of finding the IFS which best represents a given function. Multiscale techniques that are used in the analysis are discussed. Some previous results from the IFS literature are introduced. >

Image restoration using biorthogonal wavelet transform

Abstract: A well-known method to solve ill-posed problem in image restoration is to use regularization techniques. The purpose of this paper is to propose a new scheme for digital image restoration based on a regularization method and on the BiOrthogonal Wavelet Transform. We show that, in cases where the blur function can be considered a scale function of a biorthogonal multiresolution analysis, it is possible to obtain an efficient family of regularization operators from the convolution operator alone.

Design and evaluation of a multistage object-detection approach

Abstract: Accurate detection of unique objects with minimal false alarm rates is an important requirement for most reconnaissance tasks. This paper presents a methodology for developing an object detection system which examines the spectral, spatial and topographic features in a step-wise manner. The algorithms developed are tested using high resolution thermal infrared images. Multiresolution analysis to improve the performance this approach is also discussed. Results of these experiments show a definite promise for the approach.

Applications of the fast wavelet transform

Abstract: The fast wavelet transform is an order-N algorithm, due to S. Mallat, which performs a time and frequency localization of a discrete signal. It is based on the existence of orthonormal bases ( for the space of finite-energy signals on the real line) which are constructed from translates and dilates of a single fixed function, the "mother wavelet" (the Haar system is a classical example of such a basis; recent continuous examples with compact support are due to I. Daubechies). We discuss the derivation of the Mallat wavelet transform, give some examples showing its potential for use in edge detection or texture discrimination, and finally discuss how to generate Daubechies' orthonormal bases.

Stationary Subdivision, Fractals and Wavelets

Abstract: Stationary subdivision algorithms arise in surface modeling and interrogation, image decomposition and reconstruction, as well as, in the construction of wavelets by multiresolution analysis. This paper summarizes some of the results obtained in [1] on the convergence of stationary subdivision and the structure of the limiting surface and relates them to the above topics.

Multiresolution analysis for images with a resolution factor

Abstract: J. C. FEAUVEAU LRI, Université de Paris Sud, 91405 ORSAY CEDEX, FRANCE . Thomson CSF, 1 rue des Mathurins, 92223 BAGNEUX, FRANCE . Ancien élève de l'École Normale Supérieure, Agrégé de Mathématiques (1987) . Docteur de l'Université Paris Sud spécialité Informatique (1990) . Domaine de recherche : application des techniques d'analyse multirésolution à la compression et à la segmentation d'image, théorie des ondelettes, réseaux connexionnistes .