Density tomography of rock volumes with cosmic muons involves telescopes equipped with pixelized matrices of scintillator strips able to simultaneously measure the flux of muons in hundredths of directions. The resulting muon radiography images are a measure of the amount of matter integrated along each line of sight inside the geological target. This information constitutes the primary data at the root of muon density 3-D tomography. Before being used for either interpretation or tomography inversion, the radiographies must be corrected from artefacts due to imperfect detection capacity of the detection matrices. We present a correction method based on a Bayesian inversion to construct a probabilistic model of the distorted telescope acceptance from which undistorted radiographies may be obtained. The method also allows to simultaneously derive a stochastic model for the incident flux of muons. The resulting non-linear inverse problem is solved with the Metropolis-annealing algorithm, which allows to easily implement symmetry constraints to reduce the non-uniqueness. An inversion of real data acquired with one of our field muon telescopes is presented and discussed.