Christian Pichot

Bio: Christian Pichot is an academic researcher from University of Nice Sophia Antipolis. The author has contributed to research in topics: Microwave imaging & Inverse scattering problem. The author has an hindex of 22, co-authored 81 publications receiving 2388 citations. Previous affiliations of Christian Pichot include École Normale Supérieure.

Inverse scattering: an iterative numerical method for electromagnetic imaging

Abstract: The authors propose a spatial iterative algorithm for electromagnetic imaging based on a Newton-Kantorovich procedure for the reconstruction of the complex permittivity of inhomogeneous lossy dielectric objects with arbitrary shape. Starting from integral representation of the electric field and using the moment method, this technique has been developed for 2-D (for TM and TE polarization cases) objects as well as for 3-D objects. Its performance has been compared with spectral techniques of classical diffraction tomography, the modified Newton method, and the pseudo-inverse method. >

Microwave imaging-complex permittivity reconstruction with a Levenberg-Marquardt method

Abstract: This paper refers to quantitative reconstruction of the dielectric and conductive property distributions of biological objects by means of active microwave imaging. An iterative reconstruction algorithm based on the Levenberg-Marquardt method is tested with synthetic data. The influence of the receiver geometry is investigated and two methods for choosing the regularization parameter, an empirical method and generalized cross validation (GCV) method, are examined.

Active microwave imaging of inhomogeneous bodies

Abstract: A numerical method and experimental technique for microwave imaging of inhomogenous bodies is presented. This method is based on the interpretation of the diffraction phenomena and leads to tomographic reconstruction of the body under investigation. Various numerical examples are given on spatial impulse response, recognition of dielectric rods, inhomogeneous bodies, and simulated human arm. Different experimental results on dielectric rods and isolated animal organs are also given.

Microwave imaging-Location and shape reconstruction from multifrequency scattering data

Abstract: The problem of determining the shape and location of an object embedded in a homogeneous dissipative medium from measurements of the field scattered by the object is considered in this paper. The object is assumed to be an infinite cylinder of known cross section illuminated by a TM plane wave and the scattered field is measured on a line segment perpendicular to the direction of incidence. Measurement data are carried out at three different frequencies for a homogeneous cylinder of known dielectric constant. The location and contour shape are determined using two different reconstruction algorithms, a Newton-Kantorovich (NK) method and the modified gradient (MG) method whose effectiveness and robustness are compared. Both methods are based on domain integral representations of the field in the body. They involve an iterative minimization of the defect between an integral representation of the field measured on the line and the actual measured data. The NK method involves a linearization of the nonlinear relation between the field and the contrast, as well as the solution of a direct scattering problem at each iteration. The MG method seeks the simultaneous reconstruction of the field and the characteristic function of the support of the scatterer without solving a direct problem at each step. Both methods employed the same initial guess and the a priori information that the characteristic function is nonnegative.

Microwave imaging-complex permittivity reconstruction-by simulated annealing

Abstract: A preliminary study of the application of simulated annealing (SA) to complex permittivity reconstruction in microwave tomography is presented. Reconstructions of a simplified model of a human arm obtained with simulated noise-free data are presented for three different methods: SA, quenching, and a Newton-Kantorovich method. These results show that SA can converge to an accurate solution in cases where the two deterministic methods fail. For this reason SA can be used to get closer to the final solution before applying a faster deterministic method. >

Anisotropic diffusion in image processing

Abstract: Preface Through many centuries physics has been one of the most fruitful sources of inspiration for mathematics. As a consequence, mathematics has become an economic language providing a few basic principles which allow to explain a large variety of physical phenomena. Many of them are described in terms of partial diierential equations (PDEs). In recent years, however, mathematics also has been stimulated by other novel elds such as image processing. Goals like image segmentation, multiscale image representation, or image restoration cause a lot of challenging mathematical questions. Nevertheless, these problems frequently have been tackled with a pool of heuristical recipes. Since the treatment of digital images requires very much computing power, these methods had to be fairly simple. With the tremendous advances in computer technology in the last decade, it has become possible to apply more sophisticated techniques such as PDE-based methods which have been inspired by physical processes. Among these techniques, parabolic PDEs have found a lot of attention for smoothing and restoration purposes, see e.g. 113]. To restore images these equations frequently arise from gradient descent methods applied to variational problems. Image smoothing by parabolic PDEs is closely related to the scale-space concept where one embeds the original image into a family of subsequently simpler , more global representations of it. This idea plays a fundamental role for extracting semantically important information. The pioneering work of Alvarez, Guichard, Lions and Morel 11] has demonstrated that all scale-spaces fulllling a few fairly natural axioms are governed by parabolic PDEs with the original image as initial condition. Within this framework, two classes can be justiied in a rigorous way as scale-spaces: the linear diiusion equation with constant dif-fusivity and nonlinear so-called morphological PDEs. All these methods satisfy a monotony axiom as smoothing requirement which states that, if one image is brighter than another, then this order is preserved during the entire scale-space evolution. An interesting class of parabolic equations which pursue both scale-space and restoration intentions is given by nonlinear diiusion lters. Methods of this type have been proposed for the rst time by Perona and Malik in 1987 190]. In v vi PREFACE order to smooth the image and to simultaneously enhance semantically important features such as edges, they apply a diiusion process whose diiusivity is steered by local image properties. These lters are diicult to analyse mathematically , as they may act locally like a backward diiusion process. …

Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method

Abstract: The distorted Born iterative method (DBIM) is used to solve two-dimensional inverse scattering problems, thereby providing another general method to solve the two-dimensional imaging problem when the Born and the Rytov approximations break down. Numerical simulations are performed using the DBIM and the method proposed previously by the authors (Int. J. Imaging Syst. Technol., vol.1, no.1, p.100-8, 1989) called the Born iterative method (BIM) for several cases in which the conditions for the first-order Born approximation are not satisfied. The results show that each method has its advantages; the DBIM shows faster convergence rate compared to the BIM, while the BIM is more robust to noise contamination compared to the DBIM. >

Dielectric Resonator Antennas

Abstract: Linearly and circularly polarized conformal strip-fed dielectric resonator antennas (DRAs) are studied in this article. In the latter case, a parasitic patch is used to excite a nearly degenerate mode. The hemispherical DRA, excited in its fundamental broadside TE111 mode, is used for the demonstration. In the analysis, the mode-matching method is used to obtain the Green's functions, whereas the method of moments is used to solve for the unknown strip currents. In order to solve the singularity problem of the Green's functions, a recurrence technique is used to evaluate the impedance integrals. This greatly increases the numerical efficiency. Measurements were carried out to verify the calculations, with good results. Keywords: circularly polarized antenna; dielectric antennas; mode-matching methods; moment methods; parasitic antennas; resonance

A contrast source inversion method

Abstract: This paper describes a simple algorithm for reconstructing the complex index of refraction of a bounded object immersed in a known background from a knowledge of how the object scatters known incident radiation. The method described here is versatile accommodating both spatially and frequency varying incident fields and allowing a priori information about the scatterer to be introduced in a simple fashion. Numerical results show that this new algorithm outperforms the modified gradient approach which until now has been one of the most effective reconstruction algorithms available.

A clinical prototype for active microwave imaging of the breast

Abstract: Despite its recognized value in detecting and characterizing breast disease, X-ray mammography has important limitations that motivate the quest for alternatives to augment the diagnostic tools that are currently available to the radiologist. The rationale for pursuing electromagnetic methods is strong given the data in the literature, which show that the electromagnetic properties of breast malignancy are significantly different than normal in the high megahertz to low gigahertz spectral range, microwave illumination can effectively penetrate the breast at these frequencies, and the breast is a small readily accessible tissue volume, making it an ideal site for deploying advanced near-field imaging concepts that exploit model-based image reconstruction methodology. In this paper a clinical prototype of a microwave imaging system, which actively illuminates the breast with a 16-element transceiving monopole antenna array in the 300-1000 MHz range, is reported. Microwave exams have been delivered to five women through a water-coupled interface to the pendant breast with the participant positioned prone on an examination table. This configuration has been found to be a practical, comfortable approach to microwave breast imaging. Sessions lasted 10-15 min per breast and included full tomographic data acquisition at seven different array heights beginning at the chest wall and moving anteriorly toward the nipple for seven different frequencies at each array position. This clinical experience appears to be the first report of active near-field microwave imaging of the breast and is certainly the first attempt to exploit model-based image reconstructions from in vivo breast data in order to convert the measured microwave signals into spatial maps of electrical permittivity and conductivity. While clearly preliminary, the results are encouraging and have supplied some interesting findings. Specifically, it appears that the average relative permittivity of the breast as a whole correlates with radiologic breast density categorization and may be considerably higher than previously published values, which have been based on ex vivo tissue specimens.