Suppose that one is given several images of a two-dimensional (or a multidimensional) object, but that the detail of each of these images is limited in some way. For example, the images may be projections of a multidimensional object onto a lower-dimensional space. By using sophisticated signal-processing techniques, many such limited images of a common object can be combined to construct a single enhanced image.

Techniques for combining multiple one-dimensional projections into a single two-dimensional image are known collectively as tomography (Greek toma: a cut + graphy). The term may also be used to describe techniques for combining several poor images into a single improved image. This is different from the practice of enhancing a single image by signal-processing techniques, although, of course, the two tasks are closely related.

The most widespread form of tomography, known as projection tomography, reconstructs an image from its projections. Projection tomography has a simple mathematical structure. The most familiar instance of projection tomography uses X-rays as the source of illumination and X-ray absorption as the observed phenomenon. In this case, the way the X-ray illumination is used is quite different from the case of molecular imaging where the observation in the far field is based on scattering of the illuminating X-rays. In projection tomography, the observation is based on attenuation of the illuminating rays in the geometrical-optics approximation.