Binary-constrained inversion of a buried cylindricalobstacle from complete and phaseless magneticfields

Abstract

The investigation herein is two-fold: specialization to a homogeneousobstacle of recent work (Lambert M et al 1998 Inverse Problems 14 1265-83) carried on the retrievalof an inhomogeneous cylindrical obstacle buried in a half-space in thetransverse electric (or H) polarization case; extension from the usualcase of complete wavefield data (known amplitude and phase) to the moresevere case of amplitude-only data (absent phase). The developed inversionmethod belongs to the class of modified gradient methods. The fielddistribution (here, the magnetic field) and the distribution of theobstacle parameters (here, the permittivity and conductivity) aresimultaneously sought in a search domain \U0001d49f. This is done by minimizinga two-component objective function, one of which is characterizing thesatisfaction of the wave equations within \U0001d49f, the other thedata fit. But now the electrical parameters of the sought obstacle areprescribed beforehand; this allows one to equate an appropriate complex-valuedcontrast function either to 0 (outside the obstacle) or to a known constant (inside). Two variants of abinary-constrained modified gradient algorithm are developed accordingly,tailored to either complete or phaseless data. Numericalexperimentation illustrates how they behave in a variety of obstacleconfigurations, for both exact and erroneous prescribed contrasts.