Impulse radio ultrawideband radar is a critical remote sensing tool for life detection and noncontact monitoring of vital signals. In noncontact monitoring via radar, the disturbance from respiration and environmental noise is considered critical for the estimation of heart rates. However, the heartbeat signal is generally distorted by breath harmonics and fluctuations in the time domain, and the frequencies of the vital signals are closely situated; thus, it is difficult to employ an ordinary frequency filter for separation. To solve this problem, a novel method was developed to extract heartbeat information. In this study, convolutional sparse coding, which is an unsupervised machine learning algorithm, was first used to model the heartbeat signal in the time domain, given the respiration and relative artifacts. The proposed scheme was then used to decompose the time-domain signals and directly obtain the heartbeat component by exploiting the sparsity of the heartbeat signal in the time domain. Furthermore, the performance of the proposed scheme was improved using a noise-assisted method, and the process was accelerated by learning from the K-singular value decomposition strategy. Finally, by testing the vital sign signals collected from the finite differences time-domain simulation and experiments, the results obtained indicate that the proposed approach is effective for the extraction of low-amplitude heartbeat signals from the respiration signal, and that it significantly improves the accuracy of heart rate evaluation.