Matching pursuits is a nonlinear algorithm which iteratively projects a given signal onto a complete dictionary of vectors. The dictionary is constructed such that it is well matched to the signals of interest and poorly matched to the noise, thereby affording the potential for denoising, by adaptively extracting an underlying signature from a noisy waveform. In the context of wave scattering and propagation, there are basic constituents that can be used to construct most measured waveforms. A dictionary of such constituents is used here, in the context of wave-based matching-pursuit processing of acoustic waves scattered from submerged elastic targets. It is demonstrated how wave-based matching pursuits can be utilized for denoising as well as to effect a detector, the latter being parametrized via its receiver operating characteristic (ROC). Results are presented using measured aspect-dependent (orientation-dependent) scattered waveforms, for the case of a submerged elastic shell.