Illposed inverse problems and logarithmic continuity in electromagnetics
Abstract
Examples of linear illposed 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 signaltonoise 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.
 Publication:

International Symposium on Electromagnetic Waves
 Pub Date:
 1981
 Bibcode:
 1981emw..symp..313B
 Keywords:

 Continuity (Mathematics);
 Data Reduction;
 Electromagnetic Wave Transmission;
 Error Analysis;
 Least Squares Method;
 Numerical Stability;
 Bandwidth;
 Cauchy Problem;
 Helmholtz Equations;
 Inverse Scattering;
 Logarithms;
 Reciprocity Theorem;
 Wave Diffraction;
 Communications and Radar