We present a computationally efficient and numerically robust solution to the problem of removing artifacts due to precordial compressions and ventilations from the human electrocardiogram (ECG) in an emergency medicine setting. Incorporated into automated external defibrillators, this would allow for simultaneous ECG signal analysis and administration of precordial compressions and ventilations, resulting in significant clinical improvement to the treatment of cardiac arrest patients. While we have previously demonstrated the feasibility of such artifact removal using a multichannel Wiener filter, we here focus on an efficient matching pursuit-like approach making practical real-time implementations of such a scheme feasible for a wide variety of sampling rates and filter lengths. Using more realistic data than what have been previously available, we present evidence showing the excellent performance of our approach and quantify its computational complexity.