Local reconstruction from the spherical Radon transform in 3D

In this article we study the spherical mean Radon transform in ${\mathbf{R}}^3$ with detectors centered on a plane. We use the consistency method suggested by the author of this article for the inversion of the transform in 3D. A new iterative inversion formula is presented. This formula has the benefit of being local and is suitable for practical reconstructions. The inversion of the spherical mean Radon transform is required in mathematical models in thermo- and photo-acoustic tomography, radar imaging, and others.