Binary-constrained inversion of a buried cylindrical obstacle from complete and phaseless magnetic fields

The investigation herein is two-fold: specialization to a homogeneous obsta cle of recent work (Lambert M et al 1998 Inverse Problems 14 1265-83) carri ed on the retrieval of an inhomogeneous cylindrical obstacle buried in a ha lf-space in the transverse electric (or H) polarization case: extension fro m the usual case of complete wavefield data (known amplitude and phase) to the more severe case of amplitude-only data (absent phase). The developed i nversion method belongs to the class of modified gradient methods. The held distribution (here, the magnetic field) and the distribution of the obstac le parameters (here, the permittivity and conductivity) are simultaneously sought in a search domain D. This is done by minimizing a two-component obj ective function, one of which is characterizing the satisfaction of the wav e equations within D, the other the data fit. But now the electrical parame ters of the sought obstacle are prescribed beforehand; this allows one to e quate an appropriate complex-valued contrast function either to 0 (outside the obstacle) or to a known constant M-D (inside). Two variants of a binary -constrained modified gradient algorithm are developed accordingly, tailore d to either complete or phaseless data. Numerical experimentation illustrat es how they behave in a variety of obstacle configurations, for both exact and erroneous prescribed contrasts.