  Several cardiovascular diseases are caused from localised abnormal blood flow
such as in the case of stenosis or aneurysms. Prevailing theories propose that
the development is caused by abnormal wall-shear stress in focused areas.
Computational fluid mechanics have arisen as a promising tool for a more
precise and quantitative analysis, in particular because the anatomy is often
readily available even by standard imaging techniques such as magnetic
resolution and computed tomography angiography. However, computational fluid
mechanics rely on accurate boundary conditions which is difficult to obtain. In
this paper we address the problem of recovering high resolution information
from noisy, low-resolution measurements of blood flow using variational data
assimilation (also known as 4DVar). We show that accurate flow reconstruction
is obtained with proper regularisation even in the presence of significant
noise and for a range of regularisation parameters spanning orders of
magnitude. Numerical experiments are performed in both 2D and 3D and with
pulsatile flow relevant for physiological flow in cerebral aneurysms.
