The non-Bayesian detection of an anomaly from a single or a few noisy tomographic projections is considered as a statistical hypotheses testing problem. It is supposed that a radiography is composed of an imaged nonanomalous background medium, considered as a deterministic nuisance parameter, with a possibly hidden anomaly. Because the full voxel-by-voxel reconstruction is impossible, an original tomographic method based on the parametric models of the nonanomalous background medium and radiographic process is proposed to fill up the gap in the missing data. Exploiting this "parametric tomography," a new detection scheme with a limited loss of optimality is proposed as an alternative to the nonlinear generalized likelihood ratio test, which is untractable in the context of nondestructive testing for the objects with uncertainties in their physical/geometrical properties. The theoretical results are illustrated by the processing of real radiographies for the nuclear fuel rod inspection.