Electrocardiogram (ECG) data is compressible at high compression ratios using suitable compressive sensing techniques. Methods of detecting QRS complexes in an ECG signal may comprise receiving compressively-sensed measurements of an ECG signal; constructing an estimate of the ECG signal from the received compressively-sensed measurements, and detecting QRS complexes in the estimate of the ECG signal. QRS complexes may be detected by computing the first-order difference of the estimate of the ECG signal and processing the first-order difference of the estimate of the ECG signal to locate one or more significant natural blocks, each indicating a QRS complex in the ECG signal. QRS complexes may also be detected by using a conventional QRS detection algorithm on the estimate of the ECG signal. Also disclosed are related systems for detecting QRS complexes and for compressively sensing ECG signals.