Fast and accurate transmission line outage detection can help the central control unit to respond rapidly to better maintain the security and reliability of power systems. It is especially critical in the situation of multiple line outages which is more likely to trigger cascading failures. In this article, we investigate the problem of multiple line outage detection through sparse representation based on the transient dynamics captured by Phasor Measurement Units (PMUs). An accumulation-based method is proposed to reduce the noise interference. By introducing an adaptive threshold selection rule, a modified sparse signal recovery algorithm is proposed to improve the performance of multiple line outage detection. Furthermore, an event-triggered mechanism is presented to reduce the computation burden. Finally, numerical experiments based on the IEEE Standard Test Bus System are conducted to illustrate the effectiveness of our method.