Time-frequency distributions have been used to provide high resolution representation in a large number of signal processing applications. However, high resolution and accurate instantaneous frequency (IF) estimation usually depend on the employed distribution and complexity of signal phase function. To ensure an efficient IF tracking for various types of signals, the class of complex time distributions has been developed. These distributions facilitate analysis in the cases when standard distributions cannot provide satisfactory results (e.g., for highly nonstationary signal phase). In that sense, an ambiguity based form of the forth order complex-time distribution is considered, in a new compressive sensing (CS) context. CS is an intensively growing approach in signal processing that allows efficient analysis and reconstruction of randomly undersampled signals. In this paper, the randomly chosen ambiguity domain coefficients serve as CS measurements. By exploiting sparsity in the time-frequency plane, it is possible to obtain highly concentrated IF using just small number of random coefficients from ambiguity domain. Moreover, in noisy signal case, this CS approach can be efficiently combined with the L-statistics producing robust time-frequency representations. Noisy coefficients are firstly removed using the L-statistics and then reconstructed by using CS algorithm. The theoretical considerations are illustrated using experimental results.