Compressive Sensing for Monostatic Scattering From 3-D NURBS Geometries

Compressive sensing (CS) proposes to capture compressible signals at a rate significantly smaller than the Nyquist-Shannon rate, yet allows accurate signal reconstruction. CS exploits the fact that the signal of interest is compressible by a known transform (e.g., Fourier, Wavelet, etc.) and it employs nonadaptive linear projections that preserve the structure of the signal. Approximate reconstruction is then obtained from these measurements by solving an optimization problem. In this paper, a new method that introduces ideas from CS to the method of moments (MoM) is proposed to solve electromagnetic monostatic scattering from conducting bodies of arbitrary shape efficiently modeled by nonuniform rational B-spline (NURBS) surfaces. The new method is applied to obtain monostatic induced currents and radar cross section values of several objects modeled with NURBS surfaces. The efficiency and accuracy of the new method are verified by comparing it against the multilevel fast multipole algorithm and the traditional MoM. The influences of the structure of the sparse basis functions and the number of measurements on the recovery error are also investigated.