Fully three dimensional image reconstruction from "V"-projections acquired by Compton camera with three vertex electronic collimation

The Compton camera has been proposed as an alternative to the Anger camera for SPECT. In its conventional form, the camera consists of two gamma detectors, so that incident gamma photons undergo Compton scattering in the first detector and are absorbed in the second. Coincident registration of these two interaction events defines a "cone of possibility" for the origin of a particular gamma photon. The three vertex electronic collimation requires a Compton camera with three detectors and is achieved by coincident registration of three interaction events: Compton scatterings in the first two detectors and absorption in the third detector. Because of polarization, the plane containing the three vertices defined by the interaction events tends to make a small angle with respect to the plane containing the source point and the first two vertices. This allows significant reduction of the "cone uncertainty" and better approximation of the source location by two semilines in the shape of a "V" which are the result of the intersection of the plane containing the three vertices and the cone. The data collected by such a camera are integrals over "V" shaped semilines called "V"-projections. This paper describes an approach for fully 3D image reconstruction from "V"-projections. The method is based on a special transformation, that maps a certain subset of "V"-projections into a complete set of line-projections and is used to develop both the backprojection filtering and the filtered backprojection algorithms. The results of computer simulations are presented for a Compton camera with strip geometry.