Alexandre Baussard

Adaptive multiscale reconstruction of buried objects

In this contribution, an adaptive multiscale approach for the localization and characterization of buried objects in a half-space is proposed. The main goal of the approach is to reduce the number of elements to be estimated and so the degrees of freedom in the unknown profile. This leads to improvement of the robustness of the inversion and to an increase in the quality of reconstruction. The proposed inversion scheme is based on an adaptive, coarse-to-fine iterative strategy using spline pyramids. The global procedure consists of sequences of non-linear inversions separated by refinement steps, which overall produces an accurate, low-order representation of the sought object.

HFSW Radar Model: Simulation and Measurement

High-frequency surface-wave (HFSW) radars are usually used to remotely measure oceanographic parameters. These systems can also potentially detect targets beyond the conventional microwave radar coverage. In this paper, the backscattered Doppler spectrum made up of the sea clutter, ship echoes, and the background noise has been modeled. Taking into account the propagation and the signal-processing effects, a range-Doppler image has been generated. This model can be used for different purposes like the (theoretical) evaluation of detection performance. This paper gives an overview of the theoretical elements for modeling the backscatter signal. The processing effects on the range-Doppler image and the time-evolving target signature are also introduced. Some of the simulated elements and the obtained range-Doppler images are compared with real data. Finally, from this model, the detection capabilities of HFSW radars are evaluated.

PO/Mec-Based Scattering Model for Complex Objects on a Sea Surface

In this contribution a model based on asymptotic methods is proposed to compute the scattered fleld from complex objects on a sea surface. The scattering model combines the geometrical optics, the physical optics and the method of equivalent currents. It includes the shadowing efiects and multiple-bounce up to order 3. This model is used, in the following, for Radar Cross Section (RCS) estimation and to generate Synthetic Aperture Radar (SAR) raw data for imaging applications. The theoretical aspects are reviewed in this paper and the proposed model is detailed. Numerical results are provided to validate the approach through the computation of RCS for canonical objects and complex scenes. Both the bistatic and the monostatic conflgurations are studied in this work. Finally some flrst results dealing with SAR imaging of objects on a sea surface are provided. These images are constructed from the simulated raw data thanks to a chirp scaling-based algorithm.

Eddy-current evaluation of three-dimensional flaws in flat conductive materials using a Bayesian approach

This paper deals with quantitative eddy-current non-destructive evaluation of volumetric flaws. The inversion of eddy-current data leads to detection, localization, sizing and shape reconstruction of a flaw. The eddy-current probe is constituted by a driving coil which is placed at an adapted fixed position and a pick-up coil which scans the surface above the flawed region in order to collect the data. The eddy-current probe response is linked to the local variations of the electrical conductivity of the inhomogeneous material. A numerical model follows from the discretization of the coupled integral equations by using a method of moments. To solve the resulting nonlinear inverse problem, an inversion scheme is proposed within a Bayesian estimation framework. Lack of information due to the band-pass behaviour of the forward operator is compensated by introducing prior knowledge. The advantages of this approach result from combining the information contained in the data and the a priori knowledge on the solution to be estimated. The inversion problem is transformed into an optimization problem which is dealt with using a sequence of local minimizations performed via a standard descent algorithm. In order to illustrate the behaviour and the efficiency of the proposed approach, several reconstructions from simulated data are presented.

Adaptive B-spline scheme for solving an inverse scattering problem

In this paper, we present an approach to the 2D inverse scattering problem in which the unknown object is well approximated using a small number of adaptively chosen B-spline basis functions. Rather than determining a large collection of pixel values as is commonly done, we estimate directly a much smaller knot sequence associated with a B-spline representation of the object. An iterative scheme is proposed in which, at each stage, we seek to improve our estimate of the object through the insertion and deletion of knots. A specific knot insertion procedure, based on curvature information, and a specific knot deletion method, based on data fitting, are proposed. Given a collection of knots, a nonlinear, conjugate-gradient method is employed to determine an estimate of the object. By controlling the degrees of freedom in this manner we are able to forego an explicit regularization scheme. Finally, using both computer-simulated and microwave laboratory-controlled data, we demonstrate the ability of our approach to improve upon that obtained from a more standard, pixel-based inverse scheme.

Bistatic SAR: theory and simulation

At present, the most used configuration for synthetic aperture radar imaging is the monostatic one (i.e. transmitter and receiver use the same antenna). However, the multiplication of stealth radar targets and the need for more accurate observations imply new radar imaging configurations and processing developments. The bistatic configuration, i.e. operation with separated transmitting and receiving antennas, should overcome the monostatic limitations. The transmitting antenna can also be used in a monostatic configuration, and consequently it is possible to combine monostatic and bistatic data. Bistatic data acquisition provides additional qualitative and quantitative characteristics of scattering targets. The paper presents bistatic SAR images obtained by bistatic RDA (range Doppler algorithm) processing applied to the polarized electromagnetic field detected by the receiver. The proposed model is qualitatively compared with results already published in the literature (Soumekh, M., 1998; 1999), and quantitatively validated from the analytical resolution equations.

Inversion of multi-frequency experimental data using an adaptive multiscale approach

In this contribution, an adaptive multiscale approach for the reconstruction of objects from multi-frequency microwave laboratory-controlled data is proposed. The considered coarse-to-fine iterative strategy based on spline pyramids enables us to reduce the number of elements to be estimated and, consequently, the number of degrees of freedom in the unknown profile. The robustness of the inversion is increased as well as the quality reconstruction. The procedure consists of sequences of non-linear inversions separated by refinement steps, which overall produces an accurate, low-order representation of the sought object. The main goal of this paper is to test a newly designed adaptive multiscale algorithm against the new experimental data (obtained from inhomogeneous targets) from Institut Fresnel (Marseille, France).

Asymmetric power distribution model of wavelet subbands for texture classification

The generalized Gaussian distribution (GGD) is a well established statistical model for wavelet subband characterization used in several applications. However, it is not really suitable for eventual asymmetry of probability density functions. Therefore, in this paper we propose to exploit the asymmetric power distribution (APD) which is a more general and flexible model than the GGD. The APD parameters are estimated through the maximum-likelihood estimation. A supervised texture classification problem is proposed as an application in this work. It is based on the Bayesian framework which has led to the definition of the closed form of the corresponding Kullback-Leibler divergence considered as a similarity measure. To validate the APD model, the goodness-of-fit using the classical Kolmogorov-Smirnov test is used. Finally, classification results on four databases demonstrate the interest of the proposed approach.

Accuracy studies for TDOA-AOA localization of emitters with a single sensor

This paper investigates the problem of source localization using a single sensor and multipath signals in a electromagnetic warfare (EW) context. Time difference of arrival (TDOA) and angle of arrival (AOA) measurements are used to localize transmitters. This approach is interesting in the sense that no a priori knowledge of scatterers is required. For this localization approach, the minimal number of components (emitters and reflectors) is determined. Attainable accuracies of our method for the different possible configurations are discussed using the Cramér-Rao lower bounds.

PO/MEC-based bistatic scattering model for complex objects over a sea surface

In this paper, a model based on asymptotic methods is proposed in order to compute the bistatic scattered field from a complex maritime scene. The basic idea is to combine a ray tracing-based algorithm with the physical optics technique and the method of equivalents edge currents. The sea surface is generated by using the Elfouhaily directional wave spectrum. Both the target and the sea surface are meshed with triangular patches in order to compute the scattered field. Comparisons with a method of moments -based approach are provided to validate the model through simple configurations. Then more complex scenes are investigated for different sea states.