On image reconstruction algorithms for binary electromagnetic geotomography

Abstract

In this paper we discuss the selected image reconstruction methods of binary tomography in the context of their application to geophysical imaging. We restrict our considerations to a discrete version of high-frequency electromagnetic geotomography, which we label as Binary Electromagnetic Geotomography (BEG). Basically, such an imaging technique may be applied to detect subsurface anomalies (air-filled voids) whose attenuation coefficient is very low (nearly zero-value) and considerably different from that for the background. The assumption for a binary representation of the image to be reconstructed substantially relaxes image reconstruction problems related to ill-posedness that comes from an intrinsic limitation of an angular range of projections. We test two algorithms for binary tomography, where the penalty term is based on the Markov Random Field (MRF) model. The mean-field reference distribution and mean-field annealing are applied to estimate the global maximizer of the Gibbs–Boltzmann distribution associated with the objective function. We also apply the projected gradient algorithm that uses a binary steering. Very efficient implementations of the algorithms are also given. The numerical results are presented for noise-free, noisy, and real data.