Fast data-derived fundamental spheroidal excitation models with application to UXO discrimination

Electromagnetic Methods for UXO Discrimination

“…The Standardized Excitation Approach (SEA) formulation based on fundamental spheroidal modes can calculate the sensor responses produced by a geometrically complex, materially heterogeneous object, accounting for near and far field effects and all internal interactions [7,19,21,25]. The total response to any excitation is constructed simply as an appropriate superposition of responses to defined excitation modes.…”

“…The 8-mode formulation produces slightly more accurate results than the 4-mode one; however, the difference is not great and probably not justified on the basis of cost vs. benefit. The reader is referred to the literature [8,12,19,21,24,25] for discussion of alternatives in pursuing the modal parameters. Issues include control of possible ill-conditioning when one seeks to use higher modes or those only marginally supported by the data.…”

“…Note that in this formulation the capacity limits the amount of knowledge that an example can store; problematic points are eventually "sacrificed" in the interest of good generalization. The symmetric convex quadratic programming problem (21) has no local minima, and that, along with the sparsity of the solution, make the SVM a viable and attractive classifier. The weight is given by w = ∑ i α i y i x i = ∑ i∈SV α i y i x i , the bias can be computed by applying the Karush-Kuhn-Tucker conditions to the support vectors [3,10], and the machine predicts new cases using…”

“…We use a device that follows from the realization that in both (21) and (22) the data enter the problem only in the form of Fig. 12 Two classes of points interspersed, not linearly separable, with y i = +1 for the circles and y i = −1 for the crosses.…”

“…On the other hand, practitioners in areas like handwriting recognition [2] routinely exploit the statistical, model-independent character of the SVM algorithm and apply it to "raw" data that has not been distilled into simpler or unifying parameters. Encouraged by their results, we have employed the SEA [21] as a dependable and accurate model to generate synthetic secondary fields for a collection of UXO at known depths and then used SVM regression to extract unknown depths for other instances. Figure 15 shows a frequency-domain example.…”