Compressive Sensing (CS) has successfully been applied to reconstruct sparse signals and images from few observations. For multi-component non-stationary signals characterized by instantaneous frequency laws, the sparsity exhibits itself in the time-frequency domain as well as the ambiguity domain. In this paper, the authors examine CS in the context of non-stationary array processing. They 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.