The high-frequency information of downhole vibration can record more specific details about the dynamic response of bottom hole assembly (BHA), which is conducive to analyzing downhole abnormal vibration and diagnosing drilling tool failure. However, high frequency measurements would generate a large amount of data, which is a huge challenge for data storage. To cope with this challenge, this work proposes applying compressive sensing theory to high-frequency measurement of downhole vibration signals and failure analysis of drilling tools. First, three ADCs clocked at different sub-Nyquist frequencies are used to collect and store downhole vibration signals. Then, the stored sparse vibration data is reconstructed into complete vibration signal by an improved OMP signal reconstruction algorithm. The performance of the proposed method has been investigated via a series of experiments by applying simulation and real vibration signals, which show that the proposed method can reconstruct the downhole vibration signal well and significantly reduce the pressure of acquisition and data storage. This method provides a new way to obtain the high-frequency measurement data of downhole vibration, and provides a data basis for further mastering the comprehensive law of downhole vibration, diagnosing abnormal downhole vibration, and drilling tool failure.INDEX TERMS Downhole vibration measurement, Compressed sensing, Drilling tool failure.