Matrix analysis
Discretization effects in statistical inverse problems
Journal of Complexity
The nature of statistical learning theory
The nature of statistical learning theory
Statistical inverse estimation in Hilbert scales
SIAM Journal on Applied Mathematics
On inverse problems with unknown operators
IEEE Transactions on Information Theory
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Recent results on quasi-maximum likelihood histogram sieve estimators in inverse problems for Poisson processes are generalized to B-spline sieves. The impact of discretization effects on strong L2 consistency and convergence rates are studied in detail. In particular, a "rates saturation effect", caused by discretization, is demonstrated. Finite-sample implementation is proposed and tested in a Monte Carlo experiment with the Wicksell problem, which shows a superior performance of the new approach, when compared to other methods commonly used in that context. The proposed algorithm can also be used in cases with only approximately known folding kernel.