Filtered backprojection reconstruction and redundancy in Compton camera imaging

During the acquisition process with the Compton gamma-camera, integrals of the intensity distribution of the source on conical surfaces are measured. They represent the Compton projections of the intensity. The inversion of the Compton transform reposes on a particular Fourier-Slice theorem. This paper proposes a filtered backprojection algorithm for image reconstruction from planar Compton camera data. We show how different projections are related together and how they may be combined in the tomographical reconstruction step. Considering a simulated Compton imaging system, we conclude that the proposed method yields accurate reconstructed images for simple sources. An elongation of the source in the direction orthogonal to the camera may be observed and is to be related to the truncation of the projections induced by the finite extent of the device. This phenomenon was previously observed with other reconstruction methods, e.g., iterative maximum likelihood expectation maximization. The redundancy of the Compton transform is thus an important feature for the reduction of noise in Compton images, since the ideal assumptions of infinite width and observation time are never met in practice. We show that a selection operated on the set of data allows to partially get around projection truncation, at the expense of an enhancement of the noise in the images.