  We study the problem of recovering the initial data (f, 0) of the standard
wave equation from the Neumann trace (the normal derivative) of the solution on
the boundary of convex domains in arbitrary spatial dimension. Among others,
this problem is relevant for tomographic image reconstruction including
photoacoustic tomography. We establish explicit inversion formulas of the
back-projection type that recover the initial data up to an additive term
defined by a smoothing integral operator. In the case that the boundary of the
domain is an ellipsoid, the integral operator vanishes, and hence we obtain an
analytic formula for recovering the initial data from Neumann traces of the
wave equation on ellipsoids.
