On the local minima in a tomographic imaging technique

Abstract

The reliability of a recently introduced nonlinear estimation method for tomographic imaging is discussed in full detail. It is shown how a proper choice of the functional spaces to which unknown quantities belong and the exploitation of the expected properties of the object under test and of all the available a priori information positively affect robustness against false solutions of the inversion procedure. The developed arguments allow the authors to understand causes of possible false solutions, suggesting possible countermeasures. In particular, it is shown how the proposed approach allows the authors to achieve accurate and reliable reconstructions in a set of cases larger than the range of applicability of other "false solutions free" approaches. Numerical analyses confirm the validity of the approach and the effectiveness of developed inversion procedures through practical examples.