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Regularization with Approximated L2L^2L2 Maximum Entropy Method

2 June 2009
Jean-Michel Loubes
Paul Rochet
ArXiv (abs)PDFHTML
Abstract

We tackle the inverse problem of reconstructing an unknown finite measure μ\muμ from a noisy observation of a generalized moment of μ\muμ defined as the integral of a continuous and bounded operator Φ\PhiΦ with respect to μ\muμ. When only a quadratic approximation Φm\Phi_mΦm​ of the operator is known, we introduce the L2L^2L2 approximate maximum entropy solution as a minimizer of a convex functional subject to a sequence of convex constraints. Under several assumptions on the convex functional, the convergence of the approximate solution is established and rates of convergence are provided.

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