Although being small compared to inertial acceleration, viscous component of the pressure gradient has recently emerged as a potential biomarker for aortic disease conditions including aortic valve stenosis. However, as it involves the computation of second order derivatives and viscous dissipation is locally higher in the near-wall region of the larger vessels, where the lowest local signal-to-noise ratios are encountered, the estimation process from medical image velocity data through mathematical models is highly challenging. We propose a fully automatic framework to recover the laminar viscous pressure gradient through reconstruction of the velocity vector field in the aortic boundary region. An in-silico study is conducted and the pressure drop is computed solving a Poisson problem on pressure using both a reconstructed and non-reconstructed velocity profile near the vessel walls, showing a global improvement of performance with the enhanced method.