Hyperbolic wavelet transform: an efficient tool for multifractal analysis of anisotropic fields∗
نویسندگان
چکیده
Global and local regularities of functions are analyzed in anisotropic function spaces, under the common framework supplied by hyperbolic wavelet bases. Local and directional regularity features are characterized by means of global quantities derived from the coefficients of hyperbolic wavelet decompositions. A multifractal analysis is introduced, that jointly accounts for scale invariance and anisotropy, and its properties are investigated.
منابع مشابه
Characterising Complexity in Solar Magnetogram Data using a Wavelet-based Segmentation Method
The multifractal nature of solar photospheric magnetic structures are studied using the 2D wavelet transform modulus maxima (WTMM) method. This relies on computing partition functions from the wavelet transform skeleton defined by the WTMM method. This skeleton provides an adaptive spacescale partition of the fractal distribution under study, from which one can extract the multifractal singular...
متن کاملA bridge between geometric measure theory and signal processing: Multifractal analysis
We describe the main features of wavelet techniques in multifractal analysis, using wavelet bases both as a tool for analysis, and for synthesis. We focus on two promising developments: On the analysis side, we introduce the quantile leader method, which allows to put into light nonconcave multifractal spectra; on the synthesis side, we study some extensions of random wavelet series which allow...
متن کاملAWavelet-based method for multifractal analysis of rough surfaces : Applications to high-resolution satellite images of cloud structure
We apply the 2D wavelet transform modulus maxima (WTMM) method to highresolution LANDSAT satellite images of cloudy scenes. The computation of the and multifractal spectra of the radiance fields confirms the relevance of the multifractal description to account for the intermittent nature of marine stratocumulus clouds. This analysis reveals that with the available set of experimental data, ther...
متن کاملWavelet leaders and bootstrap for multifractal analysis of images
Multifractal analysis is considered a promising tool for image processing, notably for texture characterization. However, practical operational estimation procedures based on a theoretically well established multifractal analysis are still lacking for image (as opposed to signal) processing. In the present contribution, a wavelet Leader based multifractal analysis, known to be theoretically str...
متن کاملMultifractal Analysis on the Sphere
A new generation of instruments in astrophysics or vision now provide spherical data. These spherical data may present a selfsimilarity property while no spherical analysis tool is yet available to characterize this property. In this paper we present a first numerical study of the extension of multifractal analysis onto the sphere using spherical wavelet transforms. We use a model of multifract...
متن کامل