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Three extensions to radio-frequency (RF) tomography for imaging of voids under wide areas of regard are presented. These extensions are motivated by three challenges. One challenge is the lateral wave, which propagates in proximity of the air-earth interface and represents the predominant radiation mechanism for wide-area surveillance, sensing of denied terrain, or close-in sensing. A second challenge is the direct-path coupling between transmitters (Txs) and receivers (Rxs), that affects the measurements. A third challenge is the generation of clutter by the unknown distribution of anomalies embedded in the ground. These challenges are addressed and solved using the following strategies: 1) A forward model for RF tomography that accounts for lateral waves expressed in closed form (for fast computation); 2) a strategy that reduces the direct-path coupling between any Tx-Rx pair; and 3) an improved inversion scheme that is robust with respect to noise, clutter, and high attenuation. A finite-difference time domain simulation of a scenario representing close-in sensing of a denied area is performed, and reconstructed images obtained using the improved and the classical models of RF tomography are compared.