The article deals with the problem of detecting moisture in the walls of historical buildings. As part of the presented research, the following four methods based on mathematical modeling and machine learning were compared: total variation, least-angle regression, elastic net, and artificial neural networks. Based on the simulation data, the systems for the reconstruction of “pixel by pixel” tomographic images were trained. In order to test the reconstructive algorithms obtained during the research, images were generated based on real measurements and simulation cases. The method comparison was performed on the basis of three indicators: mean square error, relative image error, and image correlation coefficient. The above indicators were applied to four selected variants that corresponded to various parts of the walls. The variants differed in the dimensions of the tested wall sections, the number of electrodes used, and the resolution of the 3D image meshes. In all analyzed variants, the best results were obtained using the elastic net algorithm. In addition, all machine learning methods generated better tomographic reconstructions than the classic Total Variation method.