Sparsity and Compressed Sensing in Mono-Static and Multi-Static Radar Imaging

Abstract

This chapter is concerned with the application of sparsity and compressed sensing ideas in imaging radars, also known as synthetic aperture radars (SARs). We provide a brief overview of how sparsity-driven imaging has recently been used in various radar imaging scenarios. We then focus on the problem of imaging from undersampled data, and point to recent work on the exploitation of compressed sensing theory in the context of radar imaging. We consider and describe in detail the geometry and measurement model for multi-static radar imaging, where spatially distributed multiple transmitters and receivers are involved in data collection from the scene to be imaged. The mono-static case, where transmitters and receivers are collocated is treated as a special case. For both the mono-static and the multi-static scenarios we examine various ways and patterns of undersampling the data. These patterns reflect spectral and spatial diversity trade-offs. Characterization of the expected quality of the reconstructed images in these scenarios prior to actual data collection is a problem of central interest in task planning for multi-mode radars. Compressed sensing theory argues that the mutual coherence of the measurement probes is related to the reconstruction performance in imaging sparse scenes. With this motivation we propose a closely related, but more effective parameter we call the \(t_\%\)-average mutual coherence as a sensing configuration quality measure and examine its ability to predict reconstruction quality in various mono-static and ultra-narrow band multi-static configurations.