Theoretical and experimental study of through-wall microwave tomography inverse problems

We consider the problem of building structure estimation using microwave ray tomography. A Bayesian formulation is developed, and a Markov chain Monte Carlo (MCMC) procedure is used to sample the posterior distribution, which is based on a data likelihood defined in terms of a residual misfit between observed and predicted waveforms. To accelerate model optimization, a simulated annealing approach is combined with the MCMC, using specific model moves to explore each component of the model space. Our approach is applicable to data acquired in the frequency or time domain and for monostatic or bistatic acquisition modes. Experimental data for a multi-wall laboratory test structure were acquired using a horn antenna connected to a vector network analyzer and used to validate both the forward model and the inversion approach. Although, in true remote sensing problems for building structure, the model order is usually unknown, in this initial study, the actual inversion experiment is performed in a reduced-dimension model space for which a subset of the variables are taken as known or fixed. Generalization to the variable-dimension problem can be achieved by using reversible jump MCMC sampling procedures.