An EIT or differential EIT method in which measurements of voltage differences between electrodes are performed according to a measurement configuration in which at least one of the electrodes injecting a current in the medium being investigated is also used for performing a measurement of the voltage difference. The contact impedances of the different electrodes are measured thanks to a counter-electrode having a contact area with the medium much higher than the contact area of a unit electrode. The measurement of a contact impedance is performed by impedance spectroscopy by comparison with the impedance spectrum of an equivalent circuit. The contact impedances allow voltage drops in the injection electrodes to be calculated the voltage differences between these electrodes and to be corrected. Alternatively, the contact impedances can be used to correct or complete the direct model.