In this paper, a new methodology is presented for detecting anomalies from radiographic images. This methodology exploits a statistical model adapted to the content of radiographic images together with the hypothesis testing theory. The main contributions are the following. First, by using a generic model of radiographies based on the acquisition pipeline, the whole non-destructive testing process is entirely automated and does not require any prior information on the inspected object. Second, by casting the problem of defects detection within the framework of testing theory, the statistical properties of the proposed test are analytically established. This particularly permits the guaranteeing of a prescribed false-alarm probability and allows us to show that the proposed test has a bounded loss of power compared to the optimal test which knows the content of inspected object. Experimental results show the sharpness of the established results and the relevance of the proposed approach.