Shape Reconstruction and Other Inverse Problems

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This project seeks to further the state of the/DIV art in the numerical solution of linear and nonlinear inverse/DIV problems. This is a rich area of research/DIV with applications to a great many problems in science and/DIV engineering. In particular, one area of interest in the project is the large class of inverse problems involving/DIV moments. For instance, the problem of reconstructing the shape of a/DIV planar region given its moments is a challenging mathematical and/DIV numerical problem, with applications in computed tomography,/DIV geophysical prospecting, and thermal imaging, to name just a few./DIVGenerally, the solution of (ill-posed) inverse problems/DIV requires the use of advanced computational techniques. For instance,/DIV the efficient solution of linear and nonlinear least squares problems,/DIV and the concept of regularization of such problems are important in many /DIVapplications. It is widely recognized that the choice of a/DIV regularizing functional and the regularization parameters are both/DIV central to the success of a stable numerical inversion approach. The/DIV project is concerned with the numerically stable solution/DIV of ill-posed inverse problems, particularly those involving/DIV moments. A specific problem is that of recovering a 2-dimensional/DIV shape from its moments, involving /DIV(1) formulation and solution of regularized inversion schemes for the/DIV reconstruction of shape from moments, and (2) applying these/DIV algorithms to the reconstruction of gravitational anomalies from/DIV measurements of gravitational fields