Electrocardiogram (ECG) is widely used to provide early warning signals for cardiovascular diseases. However, traditional twelve-lead ECG monitoring methods and smartwatch-based home solutions are unable to achieve daily long-term monitoring. Therefore, in this work, we propose a system to reconstruct ECG signals from non-contact Ballistocardiogram (BCG) signals. First, we synchronously collect BCG and ECG signals using fiber optic sensors and an ECG machine, and preprocess the signals to obtain a training set. We train the Att-SNGAN model using this training set to reconstruct ECG signals from BCG inputs. Experimental results show that the reconstructed ECG signals have a mean absolute error (MAE) of only 0.0651, a Root Mean Square Error (RMSE) of 0.0735 and a Fréchet Distance (FD) of 0.0342, showing high consistency with the original ECG. This work highlights the significant potential of the system for continuous cardiac cycle monitoring and HRV analysis, providing new solutions for long-term ECG monitoring at home.