We study the reconstruction of a 3D image from a limited set of radiographs. In nondestructive testing of materials, such 3D images represent the map of attenuation of the inspected material. The reconstruction task is very useful to detect the presence of localized objects inside the material (e.g., air anomalies inside a metal), and to localize their position. We introduce parametric image models, based on a voxel decomposition of the volume, and we perform voxel estimation in the maximum a posteriori sense. In particular, we develop a sparse parametrization of the localized object areas, relying on the detection and exclusion of background (i.e., metal) voxels. Then, we perform sparse image reconstruction by designing a multiresolution scheme. This scheme successively reconstructs coarse-to-fine resolution images, and affords automatic detection of localized object voxels at each resolution level. The global image reconstruction task is then performed within a very low computation time. We finally show the performance of our method on limited angle synthetic data, in terms of quality of reconstruction and of reconstruction time.