Signals with time-varying frequency content are generally best represented in the time frequency (TF) domain, with the components instantaneous frequency laws being their key nonstationary features. There are a number of methods for TF distribution calculation (TFD), however, most of them add unwanted artifacts, making the TFD interpretation more difficult. In this paper, we use a compressive sensing approach to suppress or completely eliminate those artifacts. Furthermore, a basis pursuit algorithm is employed for signal reconstruction in order to reduce resolution loss, which is a mayor obstacle of existing TFD design methods.