Linear and Nonlinear Inverse Problems

摘要: An important aspect of the physical sciences is to make inferences about paramcters from data. In general, laws physics provide means for computing data values given a model. This called “forward problem”, see figure 1. inverse problem, aim reconstruct model set measurements. ideal case, an exact theory exists that prescribes how should be transformed in order reproduce For some selected examples such assuming required infinite and noise-free sets would available. A quantum mechanical potential one spatial dimension can reconstructed when reflection coefficient known all energies [Marchenko, 1955; Burridge, 1980]. technique generalized reconstruction three dimensions [Newton, 1989], but case redundant reasons are not well understood. The mass-density one-dimensional string constructed measurements eigenfrequencies [Borg, 1946], due symmetry this problem only even part determined. If seismic velocity earth depends on depth, exactly measurement arrival time as function distance waves using Abel transform [Herglotz, 1907], [Wiechert, 1907].