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Full-Text Articles in Physical Sciences and Mathematics
Convergence Of Algorithms For Reconstructing Convex Bodies And Directional Measures, Richard J. Gardner, Markus Kiderlen, Peyman Milanfar
Convergence Of Algorithms For Reconstructing Convex Bodies And Directional Measures, Richard J. Gardner, Markus Kiderlen, Peyman Milanfar
Mathematics Faculty Publications
We investigate algorithms for reconstructing a convex body K in Rn from noisy measurements of its support function or its brightness function in k directions u1, . . . , uk. The key idea of these algorithms is to construct a convex polytope Pk whose support function (or brightness function) best approximates the given measurements in the directions u1, . . . , uk (in the least squares sense). The measurement errors are assumed to be stochastically independent and Gaussian. It is shown that this procedure is (strongly) consistent, meaning that, …