Single measurement experimental data for an inverse medium problem inverted by a multi-frequency globally convergent numerical method

摘要

The recently developed globally convergent numerical method for an inversemedium problem for the Helmholtz equation is tested on experimental data. Thedata were originally collected in the time domain, whereas the method works inthe frequency domain with the multi-frequency data. Due to a huge discrepancybetween the collected and computationally simulated data, the straightforwardFourier transform of the experimental data does not work. Hence, it isnecessary to develop a heuristic data preprocessing procedure. This procedureis described. The preprocessed data are used as the input for the inversionalgorithm. Numerical results demonstrate good accuracy in the reconstruction ofboth refracive indices and locations of targets. Furthermore, thereconstruction errors for refractive indices of dielectric targets aresignificantly less than errors of a posteriori direct measurements.