Inversion of Spherical Means and the Wave Equation in Even Dimensions

Source abstract

We establish inversion formulas of the so-called filtered back-projection type to recover a function supported in the ball in even dimensions from its spherical means over spheres centered on the boundary of the ball. We also find several formulas to recover initial data of the form $(f,0)$ (or $(0,g)$) for the free space wave equation in even dimensions from the trace of the solution on the boundary of the ball, provided that the initial data has support in the ball.