A. Roger

Bio: A. Roger is an academic researcher. The author has contributed to research in topics: Stability (learning theory) & Numerical integration. The author has an hindex of 1, co-authored 1 publications receiving 291 citations.

Newton-Kantorovitch algorithm applied to an electromagnetic inverse problem

Abstract: An efficient algorithm is presented to compute the shape of perfectly conducting cylinders via knowledge of scattering cross sections. This choice of scattering data avoids the difficulties linked with the phase measurements or reconstructions. The mathematical analysis is performed in terms of operator and functions, and the fundamental instability of the problem is demonstrated. Then the stability is restored by means of a Tikhonov-Miller regularization. The efficiency of the method is outlined by numerical examples. References are given which show that the same algorithm applies to other electromagnetic inverse problems, especially to gratings.

Ill-posed problems in early vision

Abstract: Mathematical results on ill-posed and ill-conditioned problems are reviewed and the formal aspects of regularization theory in the linear case are introduced. Specific topics in early vision and their regularization are then analyzed rigorously, characterizing existence, uniqueness, and stability of solutions. A fundamental difficulty that arises in almost every vision problem is scale, that is, the resolution at which to operate. Methods that have been proposed to deal with the problem include scale-space techniques that consider the behavior of the result across a continuum of scales. From the point of view of regulation theory, the concept of scale is related quite directly to the regularization parameter lambda . It suggested that methods used to obtained the optimal value of lambda may provide, either directly or after suitable modification, the optimal scale associated with the specific instance of certain problems. >

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.

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. >

Design sensitivity analysis: Overview and review

Abstract: Design sensitivity plays a critical role in inverse and identification studies, as well as numerical optimization, and reliability analysis. Herein, we review the state of design sensitivity analysis as it applies to linear elliptic systems. Both first- and second-order sensitivities are derived as well as first-order sensitivities for symmetric positive definite eigenvalue systems. Although these results are not new, some of the derivations offer a different perspective than those previously presented. This article is meant as a tutorial, and as such, a simple two-degree-of-freedom spring system is employed to exemplify the sensitivity analyses. However, the concepts presented in this trivial example may be readily extended to compute sensitivities for complex systems via numerical techniques such as the finite element, boundary element, and finite difference methods.