Pulse-wave velocity (PWV) can be used to quantify arterial stiffness, allowing for a diagnosis of this condition. Multi-beam laser-doppler vibrometry offers a cheap, non-invasive and user-friendly alternative to measuring PWV, and its feasibility has been previously demonstrated in the H2020 project CARDIS. The two handpieces of the prototype CARDIS device measure skin displacement above main arteries at two different sites, yielding an estimate of the pulse-transit time (PTT) and, consequently, PWV. The presence of multiple beams (channels) on each handpiece can be used to enhance the underlying signal, improving the quality of the signal for PTT estimation and further analysis. We propose two methods for multi-channel LDV data processing: beamforming and beamforming-driven ICA. Beamforming is done by an SNR-weighted linear combination of the time-aligned channels, where the SNR is blindly estimated from the signal statistics. ICA uses the beamformer to resolve its inherent permutation and scale ambiguities. Both methods yield a single enhanced signal at each handpiece, where spurious peaks in the individual channels as well as stochastic noise are well suppressed in the output. Using the enhanced signals yields individual PTT estimates with a low spread compared to the baseline approach. While the enhancement is introduced in the context of PTT estimation, the approaches can be used to enhance signals in other biomedical applications of multi-channel LDV as well.