Electrocardiogram (ECG) signals are vital tools in assessing the health of the mother and the fetus during pregnancy. Extraction of fetal ECG (FECG) signal from the mother's abdominal recordings requires challenging signal processing tasks to eliminate the effects of the mother's ECG (MECG) signal, noise and other distortion sources. The availability of ECG data from multiple electrodes provides an opportunity to leverage the collective information in a collaborative manner. We propose a new scheme for extracting the fetal ECG signals from the abdominal ECG recordings of the mother using the multiple measurement vectors approach. The scheme proposes a dual dictionary framework that employs a learned dictionary for eliminating the MECG signals through sparse domain representation and a wavelet dictionary for the noise reduced sparse estimation of the fetal ECG signals. We also propose a novel methodology for inferring a single estimate of the fetal ECG source signal from the individual sensor estimates. Simulation results with real ECG recordings demonstrate that the proposed scheme provides a comprehensive framework for eliminating the mother's ECG component in the abdominal recordings, effectively filters out noise and distortions, and leads to more accurate recovery of the fetal ECG source signal compared to other state-of-the-art algorithms.