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- Fadil Santosa
- 1996

An approach for solving inverse problems involving obstacles is proposed. The approach uses a level-set method which has been shown to be eeective in treating problems of moving boundaries, particularly those that involve topological changes in the geometry. We develop two computational methods based on this idea. One method results in a nonlinear… (More)

The purpose of this investigation is to understand situations under which an enhancement method succeeds in recovering an image from data which are noisy and blurred. The method in question is due to Rudin and Osher. The method selects, from a class of feasible images, one that has the least total variation. Our investigation is limited to images which have… (More)

- A Litman, D Lesselier, F Santosa
- 1998

We are concerned with the retrieval of the unknown cross section of a homogeneous cylindrical obstacle embedded in a homogeneous medium and illuminated by time-harmonic electromagnetic line sources. The dielectric parameters of the obstacle and embedding materials are known and piecewise constant. That is, the shape (here, the contour) of the obstacle is… (More)

- Peter G Kaup, Fadil Santosa, Michael Vogelius
- 1996

The problem of quantitative nondestructive evaluation of corrosion in plates is considered. The inpection method uses boundary measurements of currents and voltages to determine the material loss caused by corrosion. The development of the method is based on linearization and the assumption that the plate is thin. The behavior of the method is examined in… (More)

The problem of creating eigenfunctions which are localized arises in the study of photonic bandgap structures. A model problem, that of finding material inhomogeneity in a domain so that one of its Dirichlet eigenfunctions is localized, is considered in this work. The most difficult aspect, that of formulating the problem, is described, and well-posed… (More)

A reliable and efficient computational algorithm for restoring blurred and noisy images is proposed. The restoration process is based on the minimal total variation principle introduced by Rudin et al. For discrete images, the proposed algorithm minimizes a piecewise linear l (1) function (a measure of total variation) subject to a single 2-norm inequality… (More)

- Yuying Li, Fadil Santosa
- 1994

A computational algorithm is proposed for image enhancement based on total variation minimization with constraints. This constrained minimization problem is introduced by Rudin et al [13, 14, 15] to enhance blurred and noisy images. Our computational algorithm solves the constrained minimization problem directly by adapting the affine scaling method for the… (More)

The classical level set method, which represents the boundary of the unknown geometry as the zero-level set of a function, has been shown to be very effective in solving shape optimization problems. The present work addresses the issue of using a level set representation when there are simple geometrical and topological constraints. We propose a logarithmic… (More)

Many problems in engineering design involve optimizing the geometry to maximize a certain design objective. Geometrical constraints are often imposed. In this paper, we use the level set method devised in (Osher and Sethian, to construct a simple numerical approach for problems of this type. We apply this technique to a model problem involving a vibrating… (More)