Regularization with Approximated $L^2$ Maximum Entropy Method

Details Regularization with Approximated $L^2$ Maximum Entropy Method Regularization with Approximated $L^2$ Maximum Entropy Method

2009-06-02

arxiv.org/abs/0906.0562v1

Mathematics

Statistics Theory

16 pages

Scientific paper

We tackle the inverse problem of reconstructing an unknown finite measure $\mu$ from a noisy observation of a generalized moment of $\mu$ defined as the integral of a continuous and bounded operator $\Phi$ with respect to $\mu$. When only a quadratic approximation $\Phi_m$ of the operator is known, we introduce the $L^2$ 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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