  We describe the minimax reconstruction rates in linear ill-posed equations in
Hilbert space when smoothness is given in terms of general source sets. The
underlying fundamental result, the minimax rate on ellipsoids, is proved
similarly to the seminal study by D. L. Donoho, R.~C. Liu, and B. MacGibbon,
{\it Minimax risk over hyperrectangles, and implications}, Ann.~ Statist. 18,
1990. These authors highlighted the special role of the truncated series
estimator, and for such estimators the risk can explicitly be given. We provide
several examples, indicating results for statistical estimation in ill-posed
problems in Hilbert space.
