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Abstract-We investigate the decomposition of the time-reversal operator (DORT under its French language acronym) method applied to ultrawideband electromagnetic pulses propagating in dispersive and (continuous) inhomogeneous random media where volumetric scattering effects are important. We analyze the effects of random medium statistics on the time-reversal operator (TRO) eigenvalues and eigenvectors, and on subsequent selective focusing performance. We develop and employ a full time-domain DORT by tracking the excitation eigenvectors from a singular value decomposition of the TRO over the entire bandwidth of operation. We also study effects of frequency dispersion and conduction losses on the TRO and consider dispersion/loss compensation techniques to improve DORT operation in those cases.Index Terms-Decomposition of the time-reversal operator (DORT) method, electromagnetic (EM) propagation in random media, selective focusing, time-reversal (TR).

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We introduce time-reversal ultrawideband (UWB) imaging functionals based on the simultaneous utilization of spatial and UWB frequency data acquired by limited-aspect antenna arrays. The targets are discrete scatterers embedded in homogeneous or continuous random inhomogeneous media. Singular value decomposition is applied to space-frequency multistatic scattering data matrices indexed by sensor location and frequency data, and the resulting singular values and vectors are employed to construct time-domain excitation signals for UWB imaging of the embedded scatterer(s) via synthetic backpropagation (reverse migration). Spatial information needed for focusing on the embedded scatterer(s) is provided by either the left singular vectors or the eigenvectors of the space-space multistatic data matrices. The resulting UWB imaging functionals can yield statistical stability in random media. Index Terms-Decompositionof the time reversal (TR) operator (DORT), imaging, Multiple Signal Classification (MUSIC), TR.