Body surface potential maps (BSPMs) are typically recorded from a large number of ECG leads that cover the entire thorax. This improves diagnostic accuracy and is required in Electrocardiographic imaging (ECGi). BSPMs recorded in the clinical setting may have some leads that are noisy due to poor skin electrode contact. We analyzed 117 lead BSPMs recorded from 360 subjects. We successively simulated the removal of ECG leads at various locations and tested the ability of our algorithm to accurately reconstruct the missing information. When seven electrodes were removed, the algorithm could reconstruct BSPM patterns from QRS segments with median RMSE of 6.24µV and 12.15µV and CC of 0.999 and 0.997 when Laplacian method and PCA based method were used respectively. This work shows that noisy BSPM leads, which often manifest in the clinical setting, can be more accurately reconstructed using our Laplacian based interpolation algorithm, when low number of missed electrodes in regions where electrodes are organised in a well distributed and tight mesh.