Inversion of an integral transform associated with tomography in radar detection

The integral transform, F( mu , nu )= integral _-infinity ^infinity D( eta mu , eta + nu ) exp(i mu eta ²)d eta applied to functions D(x, y) on the plane, arises when one applies tomographic reconstruction techniques to problems in radar detection. The authors show that this transform can be inverted to reconstruct the superposition D+D composed with A, where A is a fixed linear transformation of the plane. In the case relevant to applications, where D(x, y) is real valued and vanishes on the half plane x<0, D itself can be reconstructed.