Abstract
We tackle the inverse problem of reconstructing an unknown finite measure μ from a noisy observation of a generalized moment of μ defined as the integral of a continuous and bounded operator Φ with respect to μ. When only a quadratic approximation Φm of the operator is known, we introduce the L2 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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Loubes, JM., Rochet, P. (2012). Regularization with Approximated L 2 Maximum Entropy Method. In: Florack, L., Duits, R., Jongbloed, G., van Lieshout, MC., Davies, L. (eds) Mathematical Methods for Signal and Image Analysis and Representation. Computational Imaging and Vision, vol 41. Springer, London. https://doi.org/10.1007/978-1-4471-2353-8_16
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DOI: https://doi.org/10.1007/978-1-4471-2353-8_16
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