Objective: Analysis of fetal electrocardiogram (f-FCC) waveforms as well as fetal heart-rate (fHR) evaluation provide important information about the condition of the fetus during pregnancy. A continuous monitoring of f-ECG, for example using the technologies already applied for adults ECG tele-monitoring (e.g., Wireless Body Sensor Networks (WBSNs)), may increase early detection of fetal arrhythmias. In this study, we propose a novel framework, based on compressive sensing (CS) theory, for the compression and joint detection/classification of mother and fetal heart heats. Methods: Our scheme is based on the sparse representation of the components derived from independent component analysis (ICA), which we propose to apply directly in the compressed domain. Detection and classification is based on the activated atoms in a specifically designed reconstruction dictionary. Results: Validation of the proposed compression and detection framework has been clone on two publicly available datasets, showing promising results (sensitivity S = 92.5%, P += 92%, Fl = 92.2% for the Silesia dataset and S = 78%, P += 77%, Fl = 77.5% for the Challenge dataset A, with average reconstruction quality PRD = 8.5% and PRD = 7.5%, respectively). Conclusion: The experiments confirm that the proposed framework may he used for compression of abdominal f-ECG and to obtain realtime information of the fHR, providing a suitable solution for real time, very low-power f-ECC monitoring. Significance: To the authors' knowledge, this is the first time that a framework for the low-power CS compression of fetal abdominal ECG is proposed combined with a heat detector for an fHR estimation.