A Novel Inversion Method for Land Mine Imaging and Detection

摘要

We have develped, using both partial differential equation approaches and integral equation formulations, a precise method to invert acoustic or electromagnetic scattering data from macroscopic concealed objects. Our approach makes use of the ideas associated with our exact solution of partial differrential equations as described in our paper (JOSA A, Volume 13, Number 6, 1996) where we were able to collapse the number of equations by elimination of transcendentals therferoe preserving the absolute mathematical precision inherent in the patial differential equation formulation. Our mathematical method, as a consequence, has not encountered the traditional loss of preciion when inverting the scattered data. The unrestricted waveleneth range allows us to pentrate any matrial which may surround the object and differentiate between the object and the media. For this resaon we have applied our inversion scheme to landmine detection as we can penetrate and differentiate under both wet and dry conditions. Also, we are able to acount, under certain conditions, for dielectric nonlinearities of material in the concealed object. Therfore, we are able to build in density dependent false colors a 3 dimensional grid representative of both the media and of the embedded object including the internal structure of the object. We have surveyed the literature on the sujbect of recovery of physical location of concealed objects (medical imaging, industrial non-destructurive testing, military applications such as land mine detection, et etectera)_ and we have found that most of the present applications have shortcomings due to the physical changes that are present in th surrounding media or the discontinuites of physical properties of the media. For all the above reasons we believe that we may have the most versatile and mathematically precise approach to the solution of this problem.