As one of the major directions in applied and computational harmonic analysis, the classical theory of wavelets and framelets has been extensively investigated in the function setting, in particular, in the function space L2(R). A discrete wavelet transform is often regarded as a byproduct in wavelet analysis by decomposing and reconstructing functions in L2(R) via nested subspaces of L2(R) in ...

This paper presents a robust method of determining the number of texture segments in an image. We take an N ×N image and decompose it into n × n blocks. A three-scale two-dimensional discrete wavelet transform is performed on each n × n block. For each n × n block, this transformation produces coefficients for 25 wavelet channels. The energy of each channel is used as a tuple for a vector in th...

------------------------------------------------------------------ABSTRACT--------------------------------------------------------------Although the wavelet transform is powerful in representing images containing smooth areas separated with edges, it cannot perform well when the edges are smooth curves. Wavelets are less effective for images where singularities are located both in space and dir...

The surface autocorrelation function can be retrieved from the values of the far-field integrated irradiance. The inversion procedure is discussed in the frame of a theory of integrated wavelet transformation. For different types of autocorrelation functions, the capabilities and limitations of the inversion procedure are studied. The influence of experimental noise and the specific choice of t...

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7 Fig. 9. Result of the wavelet transform inversion with 3-level in solid line with the errors bars of the original data.

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In this article a new technique for the estimation of the distance of visibility in fog conditions is presented. It is based on a psychovisual model and on contrast estimation with wavelet transform. For this application, specific B–spline wavelets are introduced in order to have a good space and frequency localization and to enable a fast implementation. Using images stemming from situations o...

An algorithm for multiresolutional multisensor target identiication is presented. It uses the computationally eecient scale sequential approach to hypothesis testing during identiication and implements the inverse discrete wavelet transform to fuse data from diierent multires-olution sensors. We show that fusion leads to an increase in the probability of correct identiication without a signiica...

We give a simple method for constructing a projection from a surface of revolution M onto the plane perpendicular to the rotation axis, which preserves areas. Then we use this projection for constructing a multiresolution analysis and a continuous wavelet transform, starting from the existing planar constructions. Thus, the wavelets on M inherit all the properties of the corresponding planar wa...