Reconstruction of Concealed Objects in a Corrugated Wall With a Smoothly Varying Roughness Using the Linear Sampling Method

Abstract

Two-dimensional reconstruction of concealed objects in a wall with two-scale surface roughness is presented. The linear sampling method (LSM) as a single-frequency qualitative imaging technique is exploited. The method uses the background Green's function along with the multistatic response matrix of the overall structure. The Green's function of the wall with deterministic corrugated interfaces is derived analytically here; hence, the computations are extremely efficient. The transmission and reflection matrices of the boundaries are employed along with the generalized scattering matrix theory to find the Green's function of the geometry with the source in the wall. Since the scattering matrix of each surface is only evaluated once for the whole process, the inversion algorithm becomes very suitable for real-time applications. The method is general and could be extended to any multilayered media as well. The LSM is robust against noise and clutter; therefore, the small-scale random roughness on the interfaces does not prevent the method from detection of the objects, verified by the results.