Self-stabilizing processes based on random signs

A self-stabilizing processes {Z(t), t ∈ [t0,t1)} is a random process which when localized, that is scaled to a fine limit near a given t ∈ [t0,t1), has the distribution of an α(Z(t))-stable process, where α:ℝ→(0,2) is a given continuous function. Thus the stability index near t depends on the value of the process at t. In an earlier paper we constructed self-stabilizing processes using sums over plane Poisson point processes in the case of α:ℝ→(0,1) which depended on the almost sure absolute convergence of the sums. Here we construct pure jump self-stabilizing processes when α may take values greater than 1 when convergence may no longer be absolute. We do this in two stages, firstly by setting up a process based on a fixed point set but taking random signs of the summands, and then randomizing the point set to get a process with the desired local properties.PostprintPeer reviewe

An Interactive EA for Multifractal Bayesian Denoising

International audienceWe present in this paper a multifractal bayesian denoising technique based on an interactive EA. The multifractal denoising algorithm that serves as a basis for this technique is adapted to complex images and signals, and depends on a set of parameters. As the tuning of these parameters is a difficult task, highly dependent on psychovisual and subjective factors, we propose to use an interactive EA to drive this process. Comparative denoising results are presented with automatic and interactive EA optimisation. The proposed technique yield efficient denoising in many cases, comparable to classical denoising techniques. The versatility of the interactive implementation is however a major advantage to handle difficult images like IR or medical images

Evolutionary signal enhancement based on Hölder regularity analysis

International audienceWe present an approach for signal enhancement based on the analysis of the local Hölder regularity. The method does not make explicit assumptions on the type of noise or on the global smoothness of the original data, but rather supposes that signal enhancement is equivalent to increasing the Hölder regularity at each point

Multifractal properties of power-law time sequences; application to ricepiles

We study the properties of time sequences extracted from a self-organized critical system, within the framework of the mathematical multifractal analysis. To this end, we propose a fixed-mass algorithm, well suited to deal with highly inhomogeneous one dimensional multifractal measures. We find that the fixed mass (dual) spectrum of generalized dimensions depends on both the system size L and the length N of the sequence considered, being however stable when these two parameters are kept fixed. A finite-size scaling relation is proposed, allowing us to define a renormalized spectrum, independent of size effects.We interpret our results as an evidence of extremely long-range correlations induced in the sequence by the criticality of the systemComment: 12 pages, RevTex, includes 9 PS figures, Phys. Rev. E (in press

Generalized Multifractional Brownian Motion: Definition and Preliminary Results

The Multifractional Brownian Motion (MBM) is a generalization of the well known Fractional Brownian Motion. One of the main reasons that makes the MBM interesting for modelization, is that one can prescribe its regularity: given any Hölder function H(t), with values in ]0,1[, one can construct an MBM admitting at any t0, a Hölder exponent equal to H(t0). However, the continuity of the function H(t) is sometimes undesirable, since it restricts the field of application. In this work we define a gaussian process, called the Generalized Multifractional Brownian Motion (GMBM) that extends the MBM. This process will also depend on a functional parameter H(t) that belongs to a set , but will be much more larger than the space of Hölder functions

LOCAL REGULARITY-BASED IMAGE DENOISING

We present an approach for image denoising based on the analysis of the local Hölder regularity. The method takes the point of view that denoising may be performed by increasing the Hölder regularity at each point. Under the assumption that the noise is additive and white, we show that our procedure is asymptotically minimax, provided the original signal belongs to a ball in some Besov space. Such a scheme is well adapted to the case where the image to be recovered is itself very irregular, e.g. nowhere differentiable with rapidly varying local regularity. The method is implemented through a wavelet analysis. We show an application to SAR image denoising where this technique yields good results compared to other algorithms