An Inverse Fast Multipole Method for Geometry Reconstruction Using Scattered Field Information

Abstract

A novel inverse fast multipole method (FMM) application for accelerating inverse problem solution is presented. The idea is based on the multipole expansion properties of the scattered fields and reconstructed equivalent currents, which allow an easy inversion of the FMM operators, resulting in a forward solution of the inverse problem, i.e., without matrix inversion or cost function minimization. In addition, this technique allows the use of reconstruction domain discretization larger than half a wavelength and overcomes the restriction of having the entire target enclosed by a reconstruction domain, features that also contribute to the reduction of calculation time. Two 3D application examples are presented, highlighting the achieved inverse FMM speed-up with respect to previous inverse scattering methods for geometry reconstruction.Index Terms-Imaging, inverse methods, fast multipole method (FMM), near-field characterization, sources reconstruction method (SRM).

A Gpu Implementation of the Inverse Fast Multipole Method for Multi-Bistatic Imaging Applications

“…The IFMM algorithm is an inverse scattering technique [11], which may be used to reconstruct support and constitutive parameters of the object under test (OUT) from the acquired scattered field. The algorithm is based on backpropagating the scattered fields from the observation domain into the reconstruction or imaging domain to recover the reflectivity.…”

“…The phase-shift between the observation point r m and the center of the m obs -th observation group, C m obs is defined as e +jk 0 ( rm− Cm obs ) . Similarly, the disaggregation operator assumes that the reflectivity, sometimes defined as equivalent currents, [11], J (p) n (where n and p indicate the current and polarization index respectively in a cubic sub-domain ΔV n ) can be locally approximated as a plane wave within the source groups, n source . The phase-shift between the center of the cubic sub-domain r n and the center of the n source -th source group, C nsource is defined as e +jk 0 ( Cn source − r n ) .…”

“…However, iterative schemes in inverse problems are still time-consuming if compared to the use of inverse operators. For this reason, an inverse operator derived from the FMM, the Inverse Fast Multipole Method (IFMM) has been presented in [11,12] applied to inverse scattering and imaging problems.…”

A Multi-Gpu Sources Reconstruction Method for Imaging Applications

“…In fact, the inverse Fast Multipole Method presented in [18], achieves two orders of magnitude speedup with respect to [7]. However, this acceleration scheme is based on the far field approximation of the translation operator, which might limit its scope of application.…”

“…The speed up scheme combines inverse and forward problems, as shown in Figure 1, but overcoming the limitation introduced by Green's function far field approximation [18]. The idea is to recover an equivalent current distribution on a surface enclosing the objectunder-test (Figure 1(b)).…”