Reconstruction of object surfaces from sparse measures is an ill-posed inverse problem which requires a priori knowledge to be regularized. This problem becomes more difficult whenever an active method is used and a scattering medium is present between the signal source and the scene observed. This paper describes a reconstruction method that can be applied to solve a microwave imaging problems. The goal of the proposed algorithm is to obtain a pixel-based representation of 2-D object slices. The objects are assumed to be inhomogeneous dielectric scatterers in a microwave electromagnetic field. The method is based on the hypothesis that the observed field is a Markov Random Field (MRF), and consists in finding the field configuration that maximizes the a posteriori probability measure associated with the MRF model. A specific probabilistic measure that is based on a weak-membrane regularizing constraint as an a priori model and on an observation model using a near-field hypothesis is proposed. A classical stochastic optimization approach (i.e., simulated annealing with a Metropolis sampler) is adopted to find the probabilistic maximum. The capabilities and effectiveness of the method are evaluated and compared with those of other approaches requiring matrix inversion. Finally, simulation results are reported that show better reconstructions, than those obtained by other microwave image domain methods.
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