Characterization of the Object Buried Beneath a Random Rough Ground Using a New Semi-Analytical Mode Matching Inverse Method

Abstract

Detection and estimation of the objects buried under random rough surfaces is an inter-esting research subject because of its broad range of applications such as environmentalmonitoring[1], nondestructive testing[2] and biomedical imaging [3]. For many inverseproblems, estimating the value of all pixels in the region of interest is not required; instead,information concerning the size, shape and location of the buried objects is desired. Thesegeometric inversion methods eliminate the necessity for estimation of a dense collectionof pixel values and just concentrate on identifying the geometric structure of an unknownobject. Among all curve models, B-splines [4] have some interesting properties that makesthemoneofthemostdesirablecurvemodel;thesefunctionsaresmooth,continuous,locallycontrollable and spatially unique. More specifically, instead of working with all discretizedpoints on the boundaries, our method optimizes the control points of the boundaries de-fined by B-spline functions to accelerate the reconstruction. The inverse methods typicallyrely on forward solvers including numerical or analytical methods. Of particular interestin our work is the use of Semi-Analytic Mode Matching method (SAMM) [5] as a hybridmethod that combines the physical basis of analytic methods with the flexibility and versa-tility of numerical methods. This model is of low computational complexity compared toother approaches and highly accurate in the region of interest. In our work, we employ theLevenberg-Marquardt method [6,7] as a nonlinear least-squares minimization algorithm tooptimize the parameters defining the boundaries in compact parametric form.