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Ohmic dissipation in conductive media considerably limits the penetrative power of high-frequency electromagnetic imaging methods and implies that deep regions can be probed only with low-frequency fields. Unfortunately, these low-frequency fields are governed by a diffusive equation which prevents direct high-resolution imaging as in seismic and georadar imaging. However, a clue for high-resolution imaging in the diffusive approximation is given by a Fredholm integral equation of the first kind which links diffusive fields to their propagative duals. If these duals could be recovered by inverting this integral equation, the seismic imaging toolbox might be used, at least from a theoretical point of view, to produce fine electromagnetic images. Spectral decomposition of the integral operator shows that the inverse problem is numerically ill-posed for both noisy and/or incomplete data. High-resolution can be achieved only by adding sparsity constraints upon the sought solution to the information content of the data. This type of a priori information also strongly regularizes the inversion but implies that the inverse problem must be treated as non-linear. A numerical algorithm, designed to work in a continuous parameter space, couples both the simulated annealing and the simplex to recover the propagative field. Numerical applications for pseudo-data with additive noise reveal that reflective interfaces can be imaged even within the poorly-favourable magnetotelluric setup.
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