Compressive sensing in nonstationary array processing using bilinear transforms

Compressive sensing (CS) has successfully been applied to reconstruct sparse signals and images from few observations. For multi-component nonstationary signals characterized by instantaneous frequency laws, the sparsity exhibits itself in the time-frequency domain as well as the ambiguity domain. In this paper, we examine CS in the context of nonstationary array processing. We show that the spatial averaging of the ambiguity function across the array improves the CS performance by reducing both noise and cross-terms. The corresponding time-frequency distribution which is reconstructed through L₁ minimizations yields significant improvement in time-frequency signature localizations and characterizations.