Air target recognition is a critical step in the radar processing chain and reliable features are necessary to make a decision. The number and position of jet engines are useful features to perform a pre-classification and give a list of possible targets. To extract these features, a sparse decomposition framework for inverse synthetic aperture radar (ISAR) images is presented. With this framework different components of the target can be detected, if signal models for these parts are available. To use it for the detection of jet engines, a review of a signal model for air intakes, which was developed by Borden, is given. This model is based on the common assumption that the propagation of electromagnetic waves inside jet engines has the same dispersive behavior as inside waveguides. With this model a decomposition of a real ISAR image, measured with the tracking and imaging radar system of Fraunhofer FHR, into point-like scattering centers and jet engines is presented.