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