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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)

In total variation denoising, one attempts to remove noise from a signal or image by solving a nonlinear minimization problem involving a total variation criterion. Several approaches based on this idea have recently been shown to be very eeective, particularly for denoising functions with discontinuities. This paper analyzes the convergence of an iterative… (More)

- DAVID C. DOBSON
- 1998

An efficient method for band structure calculations in dielectric photonic crystals is presented. The method uses a finite element discretization coupled with a preconditioned subspace iteration algorithm. Numerical examples are presented which illustrate the behavior of the method. 1. Introduction. Photonic crystals are periodic structures composed of… (More)

This paper is devoted to a numerical algorithm for the maximization of band gaps in two-dimensional photonic crystals in square lattices. We first apply the finite element method to solve the eigenvalue problem, then use the piecewise constant level set (PCLS) method to maximize the band gaps. The PCLS method is very powerful for representing and modeling… (More)

A method for computing band structures for three-dimensional photonic crystals is described. The method combines a mixed nite element discretization on a uniform grid with a fast Fourier transform preconditioner and a preconditioned sub-space iteration algorithm. Numerical examples illustrating the behavior of the method are presented. 1. Introduction… (More)

In the study of photonic crystals, the question arises naturally: which crystals produce the largest band gaps? This question is investigated by means of an optimization-based evolution algorithm which, given two dielectric materials, seeks to produce a material distribution within the fundamental cell which produces a maximal band gap at a given point in… (More)

Electrical impedance tomography is a procedure by which one nds the conductivity distribution inside a domain from measurements of voltages and currents at the boundary. This work addresses the issue of stability and resolution limit of such an imaging device. We consider the realistic case where only a nite number of measurements are available. An… (More)

The problem of determining defects in structures using eddy current methods is investigated. The goal of this work is to assess the extent to which accurate quantitative information about damage can be extracted from the data. For simplicity, we consider the problem of inspecting a plate in two dimensions. Damage is modeled as a change in the plate's… (More)

The problem of approximating the band structure of electromagnetic Bloch modes in a three-dimensional periodic medium is studied. We analyze a mixed finite element approximation technique based on a variation of Nedelec edge elements. Convergence of approximate eigenvalues to those of the continuous system is proved.