Olivier Féron

Microwave imaging of inhomogeneous objects made of a finite number of dielectric and conductive materials from experimental data

We deal with an electromagnetic inverse scattering problem where the goal is to characterize unknown objects from measurements of the scattered fields that result from their interaction with a known interrogating wave in the microwave frequency range. This nonlinear and ill-posed inverse problem is tackled from experimental data collected in a laboratory-controlled experiment led at the Institut Fresnel (Marseille, France), which consist of the time-harmonic scattered electric field values measured at several discrete frequencies. The modelling of the wave–object interaction is carried out through a domain integral representation of the fields in a 2D-TM configuration. The inverse scattering problem is solved by means of an iterative algorithm tailored for objects made of a finite number of different homogeneous dielectric and/or conductive materials. The latter a priori information is introduced via a Gauss–Markov field for the distribution of the contrast with a hidden Potts–Markov field for the class of materials in the Bayesian estimation framework. In this framework, we first derive the posterior distributions of all the unknowns and, then, an appropriate Gibbs sampling algorithm is used to generate samples and estimate them. The proposed Bayesian inversion method is applied to both a linear case derived from diffraction tomography and the full nonlinear problem.

Correlation Between Homogeneous Propane Pyrolysis and Pyrocarbon Deposition

Pyrocarbon deposition through propane pyrolysis is studied in a 1-D hot-wall CVD furnace. The gas-phase pyrolysis is modeled with a partially reduced kinetic mechanism leading to polycyclic aromatic compounds (PAHs). The C2-C4 and C3 reaction paths are in competition for benzene formation. There is also an independent C3-C5 path leading to naphthalene. The gas-phase concentrations are correlated with experimental data including in situ Fourier transform infrared spectra intensities, pyrocarbon deposition rates, and pyrocarbon nanotextures. Rough laminar pyrocarbon deposition appears to be more related to PAHs than smooth laminar pyrocarbon.

Image fusion and unsupervised joint segmentation using a HMM and MCMC algorithms

In this paper we propose a Bayesian framework for unsupervised image fusion and joint segmentation. More specifically we consider the case where we have observed images of the same object through different imaging processes or through different spectral bands (multi- or hyperspectral images). The objective of this work is then to propose a coherent approach to combine these images and obtain a joint segmentation which can be considered as the fusion result of these observations. The proposed approach is based on a hidden Markov modeling of the images where the hidden variables represent the common classification or segmentation labels. These label variables are modeled by the Potts Markov random field. We propose two particular models for the pixels in each segment (iid. or Markovian) and develop appropriate Markov chain Monte Carlo algorithms for their implementations. Finally we present some simulation results to show the relative performances of these models and mention the potential applications of the proposed methods in medical imaging and survey and security imaging systems.

Bayesian approach to change points detection in time series

Change points detection in time series is an important area of research in statistics, has a long history and has many applications. However, very often change point analysis is only focused on the changes in the mean value of some quantity in a process. In this work we consider time series with discrete point changes which may contain a finite number of changes of probability density functions (pdf). We focus on the case where the data in all segments are modeled by Gaussian probability density functions with different means, variances and correlation lengths. We put a prior law on the change point occurances (Poisson process) as well as on these different parameters (conjugate priors) and give the expression of the posterior probability distributions of these change points. The computations are done by using an appropriate Markov Chain Monte Carlo (MCMC) technique.

Bayesian segmentation of hyperspectral images

In this paper we consider the problem of joint segmentation of hyperspectral images in the Bayesian framework. The proposed approach is based on a Hidden Markov Modeling (HMM) of the images with common segmentation, or equivalently with common hidden classification label variables which is modeled by a Potts Markov Random Field. We introduce an appropriate Markov Chain Monte Carlo (MCMC) algorithm to implement the method and show some simulation results.

Reconstruction of piecewise homogeneous images from partial knowledge of their Fourier Transform

Fourier synthesis (FS) inverse problem consists in reconstructing a multi‐variable function from the measured data which correspond to partial and uncertain knowledge of its Fourier Transform (FT). By partial knowledge we mean either partial support and/or the knowledge of only the module and by uncertain we mean both uncertainty of the model and noisy data. This inverse problem arises in many applications such as : optical imaging, radio astronomy, magnetic resonance imaging (MRI) and diffraction scattering (ultrasounds or microwave imaging).Most classical methods of inversion are based on interpolation of the data and fast inverse FT. But when the data do not fill uniformly the Fourier domain or when the phase of the signal is lacking as in optical interferometry, the results obtained by such methods are not satisfactory, because these inverse problems are ill‐posed. The Bayesian estimation approach, via an appropriate modeling of the unknown functions gives the possibility of compensating the lack of i...

Microwave imaging: characterization of unknown dielectric or conductive materials

Microwave imaging problem consists in reconstructing unknown objects from measurements of the scattered field that result from their interaction with a known interrogating wave. This problem is nonlinear and ill‐posed. The main classical methods to solve this inverse problem are based on the linearization of the model (by using Born or Rytov approximation) or work directly on the nonlinear mapping. In both cases the inverse problem is solved by minimizing a cost functional that can be, in a Bayesian estimation framework, interpreted as a Maximum a posteriori (MAP) estimate. The classical prior information introduced is a smoothness or contour preserving constraint. In this paper we propose to introduce the information that the object is composed of a finite (known) number of materials by using hierarchical Markov Random Field modeling approach. We then propose a Bayesian inversion method and compute the Posterior Mean estimate by using appropriate Markov Chain Monte Carlo (MCMC) algorithms.