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In underwater sensing applications it is often difficult to train a classifier in advance for all targets that may be seen during testing, due to the large number of targets that may be encountered. We therefore partition the training data into target classes, with each class characteristic of multiple targets that share similar scattering physics. In some cases one may have a priori insight into which targets should constitute a given class, while in other cases this segmentation must be done autonomously based on the scattering data. For the latter case, we constitute the classes using an information-theoretic mapping criterion. Having defined the target classes, the second phase of our identification procedure involves determining those features that enhance the similarity between the targets in a given class. This is achieved by using a GA-based feature selection algorithm, with a Kullback-Leibler (KL) cost function. The classifier employed is appropriate for multi-aspect scattering data and is based on a hidden Markov model (HMM). The performance of the class-based classification algorithm is examined using both measured and computed acoustic scattering data from submerged elastic targets. 2 1 = , for N c codes. Assuming that the target class is described by M states, the likelihood of observing code c n in state s m of target i is approximated as

Abstract-The extended Born technique is an approximate nonlinear method for analyzing scattering from a weak discontinuity. Moreover, when applied to the low-frequency (electromagnetic induction) applications for which it was developed originally, extended Born has accurately modeled scattering from inhomogeneities considerably larger than those appropriate for the standard linear Born technique. In this letter, we examine the extended Born technique at radar frequencies, considering three-dimensional (3-D) scattering from a dielectric target buried in a lossy half space.Index Terms-Born approximation, buried object detection.There are many applications for which one would like to consider electromagnetic scattering from a weak inhomogeneity in a background medium. For example, plastic anti-personnel land mines are often composed of materials with dielectric constants close to those of the background soil [1]. Such a scattering problem can be solved rigorously via the method of moments (MoM) [2], taking proper account of the half-space or layered-medium Green's function [2], [3] used to model the soil. However, while the MoM is highly accurate, it is often computationally expensive. In the context of the weak-scattering problem of interest here, we can avail ourselves of approximate modeling algorithms, which can yield accurate results while simultaneously being relatively inexpensive computationally. The Born approximation [4] is a well-known example of such a technique, it assuming that the fields inside the scatterer are the same as the incident fields, in the absence of the inhomogeneity. While this is a popular technique, it is only appropriate for relatively small inhomogeneities [4], [5]. Recently, Habashy et al. [5] have developed a new algorithm, which they demonstrated can handle inhomogeneities considerably larger than appropriate for the Born approximation. However, their previous research concentrated on very-low-frequency (kilohertz) applications, of interest in geophysics [5]. Moreover, previous results assumed a homogeneous background medium. Here we consider radar-frequency operation, for a target buried in a half-space.Consider a nonmagnetic background medium characterized by the generally inhomogeneous permittivity b (r r r). Further, assume that the permittivity (r r r) characterizes the medium when a dielectric inhomogeneity is present (i.e., The well-known Born approximation is characterized by assuming The expression in (3) yields an approximation for the electric fields inside the target, which can be used in (1) to find the fields everywhere (i.e., for r r r 6 2 V ); this approximation has been termed "extended Born" problem, we invert a single 3N 2 3N (three vector field components, each represented by a separate cube), rather than N 3 2 3 matrices.As with the MoM, the extended Born technique requires accurate computation of the dyadic Green's function G G G(r r r; r r r 0 Before proceeding, we note that the loss in the half-space is used to represent the characteristics of soil, but i...

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