Inverse Backscattering Problem for the Acoustic Equation in Even Dimensions

We show that the sound speed c x. of the acoustic wave equation in any even dimension can be uniquely determined by the backscattering data provided that it is close to a constant. In the three-dimensional case, P. Stefanov and G. Uhlmann SIAM J. Math. Anal. 28, 1997, 1191]1204.have proved a similar result. Their method takes advantage of the inversion formula for the Radon transform in odd dimensions being a local operator. This is not true in even dimensions. Moreover, the odd-dimensional Lax and Phillips modified Radon transform fails to work in even dimensions. In this paper, we overcome these difficulties and prove an even-dimensional version of Stefanov and Uhlmann’s result