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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)
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)
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)
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)
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)