Adaptive estimation of linear functionals in Hilbert scales from indirect white noise observations

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Oracle inequalities for inverse problems (2002, background): “…been studied in a number of papers [see Johnstone and Silverman (1990), Korostelev and Tsybakov (1993), Koo (1993), Donoho (1995), Mair and Ruymgaart (1996), Golubev and Khasminskii (1999, 2001), Johnstone (1999), Goldenshluger and Pereverzev (2000) and Cavalier and Tsybakov (2002) among others].”
Comparing parameter choice methods for regularization of ill-posed problems (2011, background): “Since then it has been developed further for regularization of linear inverse problems [50, 135, 105, 106, 18] and nonlinear inverse problems [12, 13] in deterministic and stochastic settings.”
Geometry of linear ill-posed problems in variable Hilbert scales Inverse Problems 19 789-803 (2003, background): “Since then many authors have adopted this approach towards various applications, we mention [27] and [4].”
Sharp adaptation for inverse problems with random noise (2002, background): “This happens, for example, if the bases ' k ; k are imposed by the structure of a particular experiment and cannot be chosen by the statistician see Math e and Pereverzev (1999), Goldenshluger and Pereverzev (1999) for further discussion and results on the rates of convergence].”