A sparse reconstruction approach capable of localizing multiple acoustic emission events is proposed. The approach is specifically designed for localizing events that occur closely in time, where triangulation methods can fail. To perform localization, the approach uses information contained in the entire length of acoustic emission signals and is implemented using the matching pursuit algorithm. Implementation is considered theoretically for large-diameter thin-walled pipes. The approach is validated on experimental data of simulated acoustic emission events in a thin-walled pipe. The experimental data correspond to helical guided ultrasonic waves generated by standard pencil lead breaks (Hsu-Nielsen sources) on its outer surface. The acoustic emission signals are recorded by sparsely distributed low-profile piezoelectric transducers instrumented on the outer surface. Experimental examples are presented for the failure of the triangulation method when multiple sources are present while highlighting the capabilities of the proposed technique. It is demonstrated that the approach possesses the ability of localizing multiple events occurring closely in time. An example is also presented for the localization of a more commonly encountered isolated acoustic emission event.