In recent years, X-ray screening systems have been used to safeguard environments in which access control is of paramount importance. Security checkpoints have been placed at the entrances to many public places to detect prohibited items such as handguns and explosives. Human operators complete these tasks because automated recognition in baggage inspection is far from perfect. Research and development on X-ray testing is, however, ongoing into new approaches that can be used to aid human operators. This paper attempts to make a contribution to the field of object recognition by proposing a new approach called Adaptive Sparse Representation (XASR+). It consists of two stages: learning and testing. In the learning stage, for each object of training dataset, several patches are extracted from its X-ray images in order to construct representative dictionaries. A stop-list is used to remove very common words of the dictionaries. In the testing stage, test patches of the test image are extracted, and for each test patch a dictionary is built concatenating the 'best' representative dictionary of each object. Using this adapted dictionary, each test patch is classified following the Sparse Representation Classification methodology. Finally, the test image is classified by patch voting. Thus, our approach is able to deal with less constrained conditions including some contrast variability, pose, intra-class variability, size of the image and focal distance. We tested the effectiveness of our method for the detection of four different objects. In our experiments, the recognition rate was more than 97% in each class, and more than 94% if the object is occluded less than 15%. Results show that XASR+ deals well with unconstrained conditions, outperforming various representative methods in the literature.