Abstract
Let f(x) be an unknown smooth image function defined on a domain G ⊂ RN . Assume that some transform Rf(z) of the image f is available at given points z1,…,zn, i.e. that the observations are of the form (9.1) Yi=Rf(zi)+ξi, i=1,…,n. The random errors are supposed to be i.i.d. (0,σ2 )-Gaussian random variables. We do not specify now the nature of the transform Rf. In the examples below Rf(z) is a real-valued function defined on a domain Z in the space RN of the same dimension as G.
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© 1993 Springer-Verlag New York, Inc.
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Korostelev, A.P., Tsybakov, A.B. (1993). Image Estimation from Indirect Observations. In: Minimax Theory of Image Reconstruction. Lecture Notes in Statistics, vol 82. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2712-0_9
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DOI: https://doi.org/10.1007/978-1-4612-2712-0_9
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-94028-1
Online ISBN: 978-1-4612-2712-0
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