Imaging in layered media

Abstract

Detection and imaging of obstacles embedded in a stratified medium find a wide application area including underground imaging and through-wall imaging (TWI) as two-layered and three-layered medium applications, respectively. Despite the fact that both subsurface imaging and TWI have been a widespread area of research, in-wall imaging has remained a relatively untouched area. The literature on this topic is very limited indicating the difficulty level of the problem, that is, the main concern of this thesis. In addition to radar techniques and inversion algorithms, direct methods to probe a structure stand out as a field of study that many applications are clustered around. Direct methods include the multiple signal classification (MUSIC) method, the linear sampling method (LSM), the factorization method, the point source method, and several others. Also, it is proven that the reverse time migration (RTM) method is of use in imaging applications. In this thesis, the RTM method is applied to the single-frequency reconstruction of embedded obstacles in a wall to perform an introductory study for in-wall imaging. The aim is to determine the geometrical properties of an object embedded in a wall by the use of an information function provided via the RTM method. The method is based on the computation of that information function separately at each point on a reconstruction domain. It is defined as the correlation levels between the incident fields emitted from the sources and the back-propagation of the scattered field. Reporting the level of achievement of the RTM method in in-wall imaging based on a single test would be misleading. It should be tested under different circumstances. For this purpose, the problem is taken from a broader perspective in order to show and confirm the effectiveness of the method. Numerical experiments within a fundamental scenario are determined in a particular order to perform an essential Monte Carlo simulation. The method is tested for different material types, locations, and structural properties of the embedded object. Both dielectric and perfect electric conductor (PEC) scatterers are taken into consideration. In other words, both weak and strong scatterers are studied. Also, different acquisition lines, operating frequencies, and noise levels are used. A comparative study should be conducted to make an objective evaluation of the achievement level of the method. In line with this, the performance level in in-wall imaging is shown in comparison with free space imaging to make a proper evaluation of the feasibility level of the method. A mathematical model is proposed to make an overall quantitative evaluation. Thus, it will be possible to make a general conclusion. Inverse crime is a challenge to be avoided which may occur in inverse scattering applications. It can be briefly described by the philosophical norm as "two wrongs do not make a right" that implies trivial solutions and meaningless achievements. It could be a sneaky trap while acquiring the data synthetically. In order to avoid inverse crime, the problem must be modeled properly. It is verily known that one usual suspect in inverse crime is the computation of mathematical expressions. Those are mostly the integral representations of field quantities and the Green's functions. Precision and accuracy must always be guaranteed at an acceptable level since the computation step is the weakest link that may lead to occur an inverse crime.