Time reversal in photoacoustic tomography and levitation in a cavity
  A class of photoacoustic acquisition geometries in n-space is considered such that the spherical mean transform admits an exact filtered back projection reconstruction formula. The reconstruction is interpreted as a time reversion mirror that reproduces exactly an arbitrary source distribution in the cavity. A series of examples of non-uniqueness of the inverse potential problem is constructed basing on the same geometrical technique. 
Victor Palamodov
math-ph math.MP