Analytical reconstruction formula for one-dimensional Compton camera

The Compton camera has been proposed as an alternative to the Anger camera in SPECT. The advantage of the Compton camera is its high geometric efficiency due to electronic collimation. The Compton camera collects projections that are integrals over cone surfaces. Although some progress has been made toward image reconstruction from cone projections, at present no filtered backprojection algorithm exists. This paper investigates a simple 2D version of the imaging problem. An analytical formula is developed for 2D reconstruction from data acquired by a 1D Compton camera that consists of two linear detectors; one behind the other. Coincidence photon detection allows the localization of the 2D source distribution to two lines in the shape of a "V" with the vertex on the front detector. A set of "V" projection data can be divided into subsets whose elements can be viewed as line-integrals of the original image added with its mirrored shear transformation. If the detector has infinite extent, reconstruction of the original image is possible using data from only one such subset. Computer-simulations were performed to verify the newly developed algorithm.