Recently, non-contact vital sign estimating devices, which are used for health monitoring, have gradually gained interest among researchers. However, most of these devices have the disadvantages of high power consumption and high cost, which limit their practicality. Therefore, a less-expensive radar-based system is suggested for long-term health monitoring. Existing radar-based vital sign estimating schemes introduce unacceptable estimating errors. In order to improve the precision and stability, we employ Newtonized Orthogonal Matching Pursuit (NOMP) algorithm. NOMP provides better estimating results compared to existing schemes in vital sign estimation tasks. However, the performance of NOMP deteriorates severely under conditions of low signal-to-noise ratio, which causes poor power efficiency. In this study, we propose deep learning (DL)-aided NOMP schemes to tackle the aforementioned issue. Our simulation results and over the air measurements suggest that DL-aided NOMP schemes are superior to existing schemes.