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This letter deals with the analysis of moving and nonstationary objects in already focused synthetic aperture radar (SAR) images. A method based on the matching pursuit (MP) algorithm is proposed to decompose the SAR signal into a set of atoms. A model of a moving object response with frequency- and angle-dependent reflectivity is introduced to design the MP atoms. Each selected atom is associated to a scatterer of the scene and is parameterized by relevant physical descriptors, leading to a multidimensional model of the object. The efficiency of this technique is demonstrated in terms of SAR response refocusing and physical parameter map derivation, using a polarimetric SAR image of a moving object lying in a natural background.