Abstract
A new formalism for scalar tomographic inversion is developed for two-dimensional radio frequency tomography. A least squares minimization of the difference between predicted and measured data is performed in order to obtain the lossless permittivity distribution. The novelty of the method is twofold. First, a multifrequency near-field two-dimensional scattering forward problem is solved via Richmond's moment method. Second, the tomographic inversion is regularized using a roughness constraint on the model permittivity. The algorithm has been tested with synthetic data. The experimental setup for acquiring the relevant data in a real-world application (viz. in situ testing of lumber quality) is under development. It is anticipated that the algorithm will work equally well on the experimental data. In the tests, the relative lossless permittivity was determined from synthetic scattered multifrequency transverse magnetic data, which had been corrupted by additive Gaussian noise. The method was able to recover the location and magnitude of permittivity anomalies without immersing the target prism in a matching fluid
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