The method of matching pursuits utilizes a nonlinear iterative procedure to project a given waveform onto a particular dictionary. For scattering problems, the most appropriate dictionary is composed of waveobjects that are consistent with the underlying wave phenomenology. A signal scattered from most targets of interest can be decomposed in terms of wavefronts, resonances, and chirps - and each of these subclasses can be further subdivided based on characteristic wave physics. Here, we investigate the efficacy of applying the method of matching pursuits with a wave-based dictionary for the processing of scattering data. The performance of this algorithm is examined for scattering data with and without additive noise.