1. A method of producing an electrical impedance tomographic image of an object, comprising the steps of: positioning a plurality of electrodes peripherally of the object in electrical contact therewith; applying an electrical signal between the ones of the plurality of electrodes of a group of at least two selected ones of the plurality of electrodes and measuring respective resulting electrical potentials at the ones of the plurality of electrodes other than the group of selected ones; successively repeating the step of applying an electrical signal, selecting the group of at least two selected ones of the plurality of electrodes to be different ones of said plurality of electrodes for each successively repeated step of applying an electrical signal; registering the measured respective electrical potentials as measured data obtained during each of a plurality of different applications of the electrical signal; and processing the measured data to provide data defining an electrical impedance tomographic image of the object comprising the steps of: using a spectral expansion of a matrix representation of a sensitivity of a measurement process of an a priori assumed approximation of the object to provide data defining a series of mutually orthogonal basis images, and deriving from the measured data relative weightings in accordance with which at least some of the basis images are to be combined to provide a reconstructed image constituting the electrical impedance tomographic image of the object.