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Electrocardiogram (ECG) sensing is an important application for the diagnosis of cardiovascular diseases. Recently, driven by the emerging technology of wearable electronics, massive wearable ECG sensors are developed, which however brings additional sources of noise contamination on ECG signals from these wearable ECG sensors. In this paper, we propose a new low-distortion adaptive Savitzky-Golay (LDASG) filtering method for ECG denoising based on discrete curvature estimation, which demonstrates better performance than the state of the art of ECG denoising. The standard Savitzky-Golay (SG) filter has a remarkable performance of data smoothing. However, it lacks adaptability to signal variations and thus often induces signal distortion for high-variation signals such as ECG. In our method, the discrete curvature estimation is adapted to represent the signal variation for the purpose of mitigating signal distortion. By adaptively designing the proper SG filter according to the discrete curvature for each data sample, the proposed method still retains the intrinsic advantage of SG filters of excellent data smoothing and further tackles the challenge of denoising high signal variations with low signal distortion. In our experiment, we compared our method with the EMD-wavelet based method and the non-local means (NLM) denoising method in the performance of both noise elimination and signal distortion reduction. Particularly, for the signal distortion reduction, our method decreases in MSE by 33.33% when compared to EMD-wavelet and by 50% when compared to NLM, and decreases in PRD by 18.25% when compared to EMD-wavelet and by 25.24% when compared to NLM. Our method shows high potential and feasibility in wide applications of ECG denoising for both clinical use and consumer electronics.