A method reconstructing the optical properties of a medium using a reconstruction system has a radiation source lighting the medium and a detector receiving a signal transmitted by the medium. The steps include lighting the medium using a radiation source, receiving by the detector of a signal emitted by the medium, and processing, for a source-detector pair, of a first distribution of the signal received by the corresponding detector. Then computing the Mellin-Laplace transform, for a given order and a given variable, of a magnitude comprising the first distribution, the order being an integer, the variable being a real number, and reconstructing optical properties of the medium using the Mellin-Laplace transform of said magnitude. The computation step includes computing a plurality of Mellin-Laplace transforms of the magnitude for distinct values of the order, and the reconstruction step is carried out from a combination of the plurality of Mellin-Laplace transforms.