Ill-posed inverse problems and logarithmic continuity in electromagnetics
Abstract
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.
- 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