This paper presents the results of a study applying the Bayesian inversion approach to<br>electromagnetic induction (EMI) data, for applications such as UXO discrimination. The cases<br>investigated feature prominent impediments to simpler treatment, namely high signal clutter and multiple<br>objects sensed simultaneously. The fundamental feature of Bayesian inversion is rational incorporation of<br>prior information into a stochastic inference algorithm, to reach the most robust posterior probability of<br>the model identity based on measured data. In UXO detection and classification, the model is a set of<br>parameters corresponding to a particular object in a particular disposition. Prior information about the<br>target or setting and the randomness of noise from different sources warrant the application of a Bayesian<br>approach in this particular inverse problem. Broadband EMI responses at different locations, in terms of<br>scattered magnetic field components in-phase and out-of-phase with the transmitted primary field, form<br>the data vector. Undoubtedly, EMI measurements are contaminated with errors in sensor positioning,<br>truncation errors in sensors and computers, metallic clutter items, ambient radio interference, etc. The<br>prior information derives from sampling excavation at a particular site, soil information, historical<br>information on use of a site, archival knowledge on different object types, forward modeling results for a<br>particular type of UXO, and other pertinent information one can collect for a given UXO cleanup project.<br>Compared to deterministic inversion algorithms, Bayesian inversion should be more advantageous for<br>dealing with an inverse or inference problem when data are contaminated by random errors, as long as<br>one can justify characterizing the prior information statistically.<br>Two kinds of problem were solved here using the Bayesian approach: (1) data contaminated with<br>random noise and (2) data for cases in which more than one UXO-sized object is in the sensor's field of<br>view at the same time. For the first case, we applied the inversion algorithms on 100 sets of synthetic<br>data; results were compared with that from simple least squares (SLS) algorithm. Comparison shows that<br>Bayesian approach can give more accurate results, given that we can provide reasonable prior information<br>and statistics on the noise. For the second case, we measured data for two cylinders at different distances<br>from one another, with signals overlapping to one degree or another. Results show that in most cases the<br>signatures of each individual contributing target can be extracted.<br>Keywords: Bayesian, unexploded ordnance (UXO), electromagnetic induction (EMI), inversion,<br>spheroid, analytical solution, multiple objects


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