A projection operator for the restoration of divergence-free vector fields

The theory of image restoration by projection onto convex sets can also be applied to the restoration of vector fields. These can have properties that restrict them to lie in well-defined closed convex sets. One of the properties, divergence freedom, is considered, and the theory and numerical implementation of its projection operator are presented. The performance of the operator is illustrated by restoring, from partial information, two simulated divergence-free vector fields. This projection operator finds an important application in the restoration of velocity fields or optical flows computed from an image sequence when the real velocity field is known, a priori to be divergence-free.<>