Method and apparatus for X-ray imaging of a body, employing a support to receive a body to be examined, a source emitting a beam of X-rays, a detector irradiated by the beam, a converter for converting the detected intensities into data, a means for turning the mounted mobile support by an angle of rotation about an axis of rotation with respect to the source and the detector and a suitably programmed computer to average the data acquired for a pair of orthogonal angles of rotation to obtain n column and m line mean values for n and m elementary segments of a band of the detector, to construct an initial image (n, m) with the n column and m line mean values, to adjust the coefficient of attenuation in each n.times.m elementary zone by a method of least squares taking into account the n column and m line mean values regarded as constraints, to repeat the previous stages for data acquired with different pairs of preferably orthogonal angles of rotation, and to average term by term the adjusted images so as to arrive at a synthesis image expressing coefficients of attenuation of the examined body.