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The muon tomography technique, based on multiple Coulomb scattering of cosmic ray muons, has been proposed as a tool to detect the presence of high density objects inside closed volumes. In this paper a new and innovative method is presented to handle the density fluctuations (noise) of reconstructed images, a well known problem of this technique. The effectiveness of our method is evaluated using experimental data obtained with a muon tomography prototype located at the Legnaro National Laboratories (LNL) of the Istituto Nazionale di Fisica Nucleare (INFN). The results reported in this paper, obtained with real cosmic ray data, show that with appropriate image filtering and muon momentum classification, the muon tomography technique can detect high density materials, such as lead, albeit surrounded by light or medium density material, in short times. A comparison with algorithms published in literature is also presented.