  In this article we study the problem of recovering the initial data of the
two-dimensional wave equation from Neumann measurements on a convex domain with
smooth boundary in the plane. We derive an explicit inversion formula of a
so-called back-projection type and deduce exact inversion formulas for circular
and elliptical domains. In addition, for circular domains, we show that the
initial data can also be recovered from any linear combination of its solution
and its normal derivative on the boundary. Numerical results of our
implementation of the derived inversion formulas are presented demonstrating
their accuracy and stability.
