  Novel experimental modalities acquire spatially resolved velocity
measurements for steady state and transient flows which are of interest for
engineering and biological applications. One of the drawbacks of such high
resolution velocity data is their susceptibility to measurement errors. In this
paper, we propose a novel filtering strategy that allows enhancement of noisy
measurements to obtain reconstruction of smooth divergence free velocity and
corresponding pressure fields, which together approximately comply to a
prescribed flow model. The main step in our approach consists of the
appropriate use of the velocity measurements in the design of a linearized flow
model which can be shown to be well-posed and consistent with the true velocity
and pressure fields up to measurement and modeling errors. The reconstruction
procedure is formulated as a linear quadratic optimal control problem and the
resulting filter has analyzable smoothing and approximation properties. We also
discuss briefly the discretization of our approach by finite element methods
and comment on the efficient solution of the linear optimality system by
iterative solvers. The capability of the proposed method to significantly
reduce data noise is demonstrated by numerical tests in which we also compare
to other methods like smoothing and solenoidal filtering.
