A Bernoulli–Gaussian Binary Inversion Method for High-Frequency Electromagnetic Imaging of Metallic Reflectors

High-frequency electromagnetic inverse scattering of conductors has many practical applications. Its goal is to reconstruct the shape of conductors from their scattered fields at some distances. When viewed from the pixelated imaging viewpoint, any pixel in the imaging domain is either a conductor or background (air); thus such an inverse scattering problem has binary solutions for all pixels. Under the high-frequency physical optics (PO) approximation, the scattered field is formulated as a linear problem in terms of a local binary shape function. A binary inversion method is proposed for the detection and shape reconstruction of a flat PEC reflector from high-frequency scattered field measurements. To exploit the underlying binary structure, a Bernoulli-Gaussian (BG) prior model is employed to perform a binary enforcement mechanism. This binary enforcement mechanism can push each pixel of the inversion domain to have a value equal to either zero or one. Then, the damped generalized approximate message passing (GAMP) is integrated with the proposed prior model to address the binary linear inverse problem from the Bayesian inference perspective. Numerical examples are presented to demonstrate the effectiveness and robustness of the proposed BG Binary Inversion method. The performance improvement of the proposed method is attributed to the exploitation of the binary prior information of the solution and GAMP technique.