Autocorrelation-Invariant Discrete-time Functions and Associated Orthogonal Sequences

International audienceThe paper studies frequency domain characterization and properties of autocorrelation discrete-time functions. Such functions may be useful in the design and synthesis of signaling waveforms with prescribed autocorrelation functions

Efficient Gram-matrix computation for irrational resonant systems using Kautz models

International audienceWe present a new method for evaluating the Gram matrix containing the inner products of repeated integrals and derivatives of irrational transfer functions via a Kautz model. The technique is particularly interesting for describing resonant systems and it has an immediate application in model order reduction

Mine Classification based on a Fuzzy Characterisation

International audienceHigh resolution sonars provide high-quality acoustic images, allowing the classification of objects from their cast shadow. For a given ground mine except mine with radial symmetry, shadow appearance generally depends on the point of view. After a segmentation step performed on images acquired along a part of a circular trajectory of the sonar around the object, we can match and superimpose binary data. The resulting image displays a fuzzy shadow region whose pixels grey-levels depend on their successive localisation in the images of the sequence, i.e. if they belong or not to the shadow region. As an extension of feature extraction in the binary case, fuzzy geometry is a practical tool to describe fuzzy regions characterised by the degree of membership of each pixel to them. After a Principal Component Analysis applied to a set of fuzzy features, encouraging results have been achieved on simulated sonar images covering both classical and stealthy mines

Mine Classification based on raw sonar data: an approach combining Fourier Descriptors, Statistical Models and Genetic Algorithms

International audienceIn the context of mine warfare, detected mines can be classified from their cast shadow. A standard solution is to perform image segmentation first (we obtain binary from graylevel image giving the label zero for pixels belonging to the shadow and the label one elsewhere), and then to perform a classification based on features extracted from the 2D-shape of the segmented shadow. Consequently, if a mistake happens during the process, it will be propagated through the following steps. In this paper, to avoid such drawbacks, we propose a novel approach where a dynamic segmentation scheme is fully classification-oriented. Actually, classification is performed directly from the raw image data. The approach is based on the combination of deformable models, genetic algorithms, and statistical image models

Gram matrix of a Laguerre model: application to model reduction of irrational transfer function

International audienceAn efficient method for evaluating inner products of repeated integrals and derivatives of a function described by a Laguerre model is presented. An immediate and promising application is model reduction of infinite-dimensional transfer functions

A 2-D Filter Specification for Sonar Image Thresholding

International audienceWe propose a new image sonar segmentation by combining two complementary competencies. On the one hand, following an image processing approach, we aim at partitioning raw image data to provide a binary image. On the other hand, we take advantage of technological knowledge such as the principle of sonar image formation. For sonar images, grey-level histogram generally presents a single mode which entails a poor separation of two theoretical modes related to reverberation and shadow subpopulations of the image. The separation of these two modes is of critical interest in a further description of objects from their cast shadows. In this paper, an optimal filter is specified by a criterion which aims at changing the statistical properties of each area while making threshold value selection from the histogram easier. While minimizing the output pixels variance, pixel values in each region concentrate around the respective average value while, simultaneously, two distinct modes appear on the histogram of the filtered image. The minimum value found between the two modes in the smoothed histogram leads to the searched threshold. In addition, we show how filter aspect depends as well on the image sonar resolution as on sonar parameters

An Alternative Method for Numerical Inversion of Laplace Transforms

International audienceBased on least-squares approximation of the rectangular pulse [1] by exponential functions, this paper presents an alternative method for performing numerical inversion of the Laplace transform. It compares favourably with the celebrated Vlach's method

Online optimization of the time scale in adaptive Laguerre-based filters

"©2000 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE."International audienceA new online method to optimize the free parameter in adaptive Laguerre-based filters is presented. It is based on the minimization of a criterion that is equivalent to an upper bound for the quadratic approximation error. The proposed technique presents a fast convergence and a good robustness

Pertinent choice of parameters for discrete Kautz approximation

International audienceKautz functions have received much attention in the recent mathematical modeling and identification literature. These functions which involve free parameters can approximate efficiently signals with strong oscillatory behavior. We consider here the choice of the free parameters in discrete (two-parameter) Kautz approximation. Using a key relationship between Kautz and Laguerre expansions we derive an upper bound for the quadratic truncation error. Minimization of this upper bound yields pertinent parameters, whose computation then requires reduced knowledge of the function to be modeled

Pertinent parameters for Kautz approximation

International audienceA procedure for determining two parameters to be used in the Kautz approximation is presented. It is based on minimisation of an upper bound of the error energ