Method for reconstructing the optical properties of a medium using a combination of a plurality of mellin-laplace transforms of a magnitude comprising a time distribution of a received signal, and associated reconstruction system

A method for reconstructing the optical properties of a medium, using a reconstruction system comprising at least one radiation source capable of lighting the medium and at least one detector capable of receiving a signal transmitted by the medium, the method including the following steps:

• lighting the medium using the radiation source,
• receiving, by the detector, the signal transmitted by the medium, and
• processing, at least one source-detector pair, of a first distribution of the signal received by the detector,
• 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,
• wherein the computing step comprises computing a plurality of Mellin-Laplace transforms of said magnitude for distinct values of the order, and in that the reconstructing step is carried out from a combination of the plurality of Mellin-Laplace transforms.