1. A method of investigating a specimen using a tomographic imaging apparatus, the tomographic imaging apparatus comprising: a specimen holder, for holding the specimen; a source, for producing a beam of radiation that can be directed at the specimen; a detector, for detecting a flux of radiation transmitted through the specimen from the source; a stage apparatus, for producing relative motion of the source with respect to the specimen, so as to allow the source and detector to image the specimen along a series of different viewing axes; and a processing apparatus, for performing a mathematical reconstruction step whereby output from the detector is compiled into a tomographic image of at least part of the specimen, and the method comprising: performing multiple iterations of the mathematical reconstruction step, each iteration comprising: using a back projection technique to produce an initial tomogram from a set of initial images, subjecting said initial tomogram to a mathematical filtering operation, thereby producing an adjusted tomogram, and using a forward projection technique on said adjusted tomogram to dissociate it into a set of calculated images; and terminating the iteration of the mathematical reconstruction step when said calculated images satisfy an acceptance criterion.