Localized random projections with applications to coherent array imaging

We consider the standard active array imaging problem and propose a novel trade-off that enables the imaging of range limited target scenes with far fewer measurements than conventional techniques by exploiting the bandwidth of the known excitation signal. Unlike standard compressed sensing, we do not assume that the scene is sparse, only that it is range limited. We abstract the proposed method as a novel matrix sketching problem that utilizes a few localized random projections in the row space of a matrix to capture the full row space. We provide mathematical guarantees on the number of such projections required. We present imaging simulation results that support our theoretical results.