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

The local Hölder function of a continuous function

AbstractThis work focuses on the local Hölder exponent as a measure of the regularity of a function around a given point. We investigate in detail the structure and the main properties of the local Hölder function (i.e., the function that associates to each point its local Hölder exponent). We prove that it is possible to construct a continuous function with prescribed local and pointwise Hölder functions outside a set of Hausdorff dimension 0

Experiments on controlled regularity fitness landscapes

We present an experimental analysis of the influence of the local irregularity of the fitness function on the behavior of a simple version of an evolutionary algorithm (EA). Previous theoretical as well as experimental work on this subject suggest that the performance of EA strongly depends on the irregularity of the fitness function. Several irregularity measures have been derived, in order to numerically characterize this type of difficulty source for EA. These characterizations are mainly based on Hölder exponents. Previous studies used a global characterization of fitness regularity (namely the global Hölder exponent), with experimental validations being conducted on test functions with uniform irregularity. The present work refines the analysis by investigating the behavior of an EA on functions displaying variable local regularity. Our experiments confirm and quantify the intuition that performance decreases as irregularity increases. In addition, they suggest a way to modify the genetic topology to accommodate for variable regularity: More precisely, it appears that the mutation parameter, which controls the size of the neighbourhood of a point, should increase when regularity decreases. These results open the way to a theoretical analysis based on local Hölder exponents, and poses several questions with respect to on-line measurements and usage of regularity for fitness functions

Denoising techniques - a comparison

Visual information transmitted in the form of digital images is becoming a major method of communication in the modern age, but the image obtained after transmission is often corrupted with noise. The received image needs processing before it can be used in applications. Image denoising involves the manipulation of the image data to produce a visually high quality image. This thesis reviews the existing denoising algorithms, such as filtering approach, wavelet based approach, and multifractal approach, and performs their comparative study. Different noise models including additive and multiplicative types are used. They include Gaussian noise, salt and pepper noise, speckle noise and Brownian noise. Selection of the denoising algorithm is application dependent. Hence, it is necessary to have knowledge about the noise present in the image so as to select the appropriate denoising algorithm. The filtering approach has been proved to be the best when the image is corrupted with salt and pepper noise. The wavelet based approach finds applications in denoising images corrupted with Gaussian noise. In the case where the noise characteristics are complex, the multifractal approach can be used. A quantitative measure of comparison is provided by the signal to noise ratio of the image

Artificial Darwinism: an overview

Genetic algorithms, genetic programming, evolution strategies, and what is now called evolutionary algorithms, are stochastic optimisation techniques inspired by Darwin’s theory. We present here an overview of these techniques, while stressing on the extreme versatility of the artificial evolution concept. Their applicative framework is very large and is not limited to pure optimisation. Artifical evolution implementations are however computationally expensive: an efficient tuning of the components and parameter of these algorithms should be based on a clear comprehension of the evolutionary mechanisms. Moreover, it is noticeable that the killer-applications of the domain are for the most part based on hybridisation with other optimisation techniques. As a consequence, evolutionary algorithms are not to be considered in competition but rather in complement to the “classical ” optimisation techniques.Les algorithmes génétiques, la programmation génétique, les stratégies d’évolution, et ce que l’on appelle maintenant en général les algorithmes évolutionnaires, sont des techniques d’optimisation stochastiques inspirées de la théorie de l’évolution selon Darwin. Nous donnons ici une vision globale de ces techniques, en insistant sur l’extrême flexibilité du concept d’évolution artificielle. Cet outil a un champ très vaste d’applications, qui ne se limite pas à l’optimisation pure. Leur mise en oeuvre se fait cependant au prix d’un coût calculatoire important, d’où la nécessité de bien comprendre ces mécanismes d’évolution pour adapter et régler efficacement les différentes composantes de ces algorithmes. Par ailleurs, on note que les applications-phares de ce domaine sont assez souvent fondées sur une hybridation avec d’autres techniques d’optimisation. Les algorithmes évolutionnaires ne sont donc pas à considérer comme une méthode d’optimisation concurrente des méthodes d’optimisation classiques, mais plutôt comme une approche complémentaire