Multilead ECG recordings, such as those obtained through Body Surface Potential Mapping (BSPM), exhibit inherent spatial coherence due to the common cardiac source and the geometry of surface electrodes. However, standard filtering methods typically process each lead independently, ignoring this spatial structure and limiting performance under noisy conditions. We introduce a spatially coherent filtering method that projects BSPM signals onto Laplace-Beltrami (LB) eigenfunctions, a set of smooth spatial modes derived from the geometry of the torso surface. This decomposition captures inter-lead relationships and enables signal processing in a domain aligned with the anatomical layout. Standard temporal filtering and baseline correction are then applied to the spectral coefficients. The method was evaluated on synthetic data generated with FECGSYN toolbox, using known ground truth and added baseline wander and white Gaussian noise, at SNR levels of –5, 5, and 15 dB. Performance was compared to lead-wise filtering using the same temporal pipeline. Across all noise levels, the proposed method consistently outperformed the lead-wise approach. At 5 dB SNR, RMSE was reduced by 64% compared to the noisy signal and by 31% relative to lead-wise filtering. Correlation improved by 24% and 5%, respectively. Visual inspection further showed better preservation of waveform morphology and amplitude across leads. These findings demonstrate that incorporating spatial structure via LB spectral decomposition enhances the robustness of ECG signal processing, even when applying standard temporal filters. The framework provides a compact and interpretable representation for multilead ECG data, with potential for broader applications beyond denoising.