Ill-posed inverse problems and logarithmic continuity in electromagnetics

Examples of linear ill-posed problems are presented, which demonstrate that they can have very large solutions corresponding to very small data. A practical implication of logarithmic continuity, the existence of resolution limits, is discussed, which is almost noise independent in a realistic range of the signal-to-noise ratio; and the size of the smallest details of the solution which can be restored with a reasonable accuracy is given. It is also demonstrated how the resolution limit can be estimated for a given problem.