Point-source transient events (PSTEs) - optical events that are both extremely fast and extremely small - pose several challenges to an imaging system. Due to their speed, accurately characterizing such events often requires detectors with very high frame rates. Due to their size, accurately detecting such events requires maintaining coverage over an extended field-of-view, often through the use of imaging focal plane arrays (FPA) with a global shutter readout. Traditional imaging systems that meet these requirements are costly in terms of price, size, weight, power consumption, and data bandwidth, and there is a need for cheaper solutions with adequate temporal and spatial coverage. To address these issues, we develop a novel compressed sensing algorithm adapted to the rolling shutter readout of an imaging system. This approach enables reconstruction of a PSTE signature at the sampling rate of the rolling shutter, offering a 1-2 order of magnitude temporal speedup and a proportional reduction in data bandwidth. We present empirical results demonstrating accurate recovery of PSTEs using measurements that are spatially undersampled by a factor of 25, and our simulations show that, relative to other compressed sensing algorithms, our algorithm is both faster and yields higher quality reconstructions. We also present theoretical results characterizing our algorithm and corroborating simulations. The potential impact of our work includes the development of much faster, cheaper sensor solutions for PSTE detection and characterization.