Radiography is a non-destructive technique that uses penetrating radiation, such as X-rays, to image the internal structure of an object by providing projections of the material content on a two-dimensional screen. Computer Tomography (CT) uses multiple-projections to reconstruct a pixelated cross-section image. The number of projections in CT has to be at least equal to the number of reconstructed pixels in order to be able to reconstruct a non-ambiguous image. However, often imaged objects have a known or uniform material content and are examined to detect anomalies or defects. Such known information can be used to reconstruct tomographic images using a limited number of projections, i.e. less than those required in CT, even though the corresponding inverse problem is incomplete (number of knowns is less than the number of unknowns). This thesis examines several methods to reconstruct tomographic images from limited objects of nominally known structure, using the few radiographic projections typically available in radiographic inspection. The methods are applied to both simulated phantoms and available mammograms, at different levels of incompleteness. Credibility-of-solution indicators are developed to measure how close a solution is to the actual configurations. It is shown that both least-squares solutions and iterative methods are able to detect anomalies using limited number of projections.