Radio tomographic imaging (RTI) is a technology for target localization by using radiofrequency (RF) sensors in a wireless network. The change of the attenuation field caused by thetarget is represented by a shadowing image, which is then used to estimate the target’s position.The shadowing image can be reconstructed from the variation of the received signal strength (RSS)in the wireless network. However, due to the interference from multi-path fading, not all the RSSvariations are reliable. If the unreliable RSS variations are used for image reconstruction, someartifacts will appear in the shadowing image, which may cause the target’s position being wronglyestimated. Due to the sparse property of the shadowing image, sparse Bayesian learning (SBL) canbe employed for signal reconstruction. Aiming at enhancing the robustness to multipath fading,this paper explores the Laplace prior to characterize the shadowing image under the frameworkof SBL. Bayesian modeling, Bayesian inference and the fast algorithm are presented to achieve themaximum-a-posterior (MAP) solution. Finally, imaging, localization and tracking experiments fromthree different scenarios are conducted to validate the robustness to multipath fading. Meanwhile,the improved computational efficiency of using Laplace prior is validated in the localization-timeexperiment as well.