arXiv subjects

Marianne Clausel

Publications and source records attributed to Marianne Clausel.

40 records · Page 3Linked to original sources

arXiv2013

Wavelet estimation of the long memory parameter for Hermite polynomial of Gaussian processes

We consider stationary processes with long memory which are non-Gaussian and represented as Hermite polynomials of a Gaussian process. We focus on the corresponding wavelet coefficients and study the asymptotic behavior of the sum of their squares since this sum is often used for estimating the long-memory parameter. We show that the limit is not Gaussian but can be expressed using the non-Gaussian Rosenblatt process defined as a Wiener Itô integral of order 2. This happens even if the original process is defined through a Hermite polynomial of order higher than 2.

math.ST↗

arXiv2012

The Monogenic Synchrosqueezed Wavelet Transform: A tool for the Decomposition/Demodulation of AM-FM images

The synchrosqueezing method aims at decomposing 1D functions as superpositions of a small number of "Intrinsic Modes", supposed to be well separated both in time and frequency. Based on the unidimensional wavelet transform and its reconstruction properties, the synchrosqueezing transform provides a powerful representation of multicomponent signals in the time-frequency plane, together with a reconstruction of each mode. In this paper, a bidimensional version of the synchrosqueezing transform is defined, by considering a well-adapted extension of the concept of analytic signal to images: the monogenic signal. The natural bidimensional counterpart of the notion of Intrinsic Mode is then the concept of "Intrinsic Monogenic Mode" that we define. Thereafter, we investigate the properties of its associated Monogenic Wavelet Decomposition. This leads to a natural bivariate extension of the Synchrosqueezed Wavelet Transform, for decomposing and processing multicomponent images. Numerical tests validate the effectiveness of the method for different examples.

math.NA↗

arXiv2012

Hyperbolic wavelet transform: an efficient tool for multifractal analysis of anisotropic textures

Global and local regularities of functions are analyzed in anisotropic function spaces, under a common framework, that of hyperbolic wavelet bases. Local and directional regularity features are characterized by means of global quantities constructed upon the coefficients of hyperbolic wavelet decompositions. A multifractal analysis is introduced, that jointly accounts for scale invariance and anisotropy. Its properties are studied in depth.

math.FA↗

arXiv2010

Large scale behavior of wavelet coefficients of non-linear subordinated processes with long memory

We study the asymptotic behavior of wavelet coefficients of random processes with long memory. These processes may be stationary or not and are obtained as the output of non--linear filter with Gaussian input. The wavelet coefficients that appear in the limit are random, typically non--Gaussian and belong to a Wiener chaos. They can be interpreted as wavelet coefficients of a generalized self-similar process.

math.PR↗