A common problem in signal processing is decomposing a signal comprised of several components into its constituent parts. This paper uses Morphological Component Analysis (MCA) to decompose experimentally collected Sediment Volume Search Sonar (SVSS) data into short-duration and longduration components. The SVSS is a synthetic aperture sonar (SAS) system designed for detection of ordnance at shallow water depths. In the implementation of MCA, Enveloped Sinusoid Parseval (ESP) frames are used to represent the signal components with sparse representations obtained via the Split Augmented Lagrangian Shrinkage Algorithm (SALSA). Ultimately, we are able to isolate late-time ringing of metallic objects both on top of and buried beneath sediment and generate sonar imagery using the two separated components to demonstrate the isolation.