Diaphragmatic electromyogram (EMGdi) contains crucial information about human respiration therefore can be used to monitor respiratory condition. Although it is practical to record EMGdi noninvasively and conveniently by placing surface electrodes over chest skin, extraction of such weak surface EMGdi (sEMGdi) from great noisy environment is a challenging task, limiting its clinical use compared with esophageal EMGdi. In this paper, a novel method is presented for extracting weak sEMGdi signal from high-noise environment based on fast independent component analysis (FastICA), constrained FastICA and a peel-off strategy. It is truly a modified version of of progressive FastICA peel-off (PFP) framework, where the constrained FastICA helps to extract and refine respiration-related sEMGdi signals, while the peel-off strategy ensures the complete extraction of weaker sEMGdi components. The method was validated using both synthetic and clinical signals. It was demonstrated that our method was able to extract clean sEMGdi signals efficiently with little distortion. It outperformed state-of-the-art comparison methods in terms of sufficiently high SIR and CORR at all noise levels when tested on synthetic data, while also achieved an accuracy of 95.06% and a F2-score of 96.73% for breath identification on clinical data. The study presents a valuable solution for noninvasive extraction of sEMGdi signals, providing a convenient and valuable way of ventilator synchrony with a significant potential in aiding respiratory rehabilitation and health.