Enhancement of Compton camera images reconstructed by inversion of a conical Radon transform

Abstract

We present a new inversion formula for a weighted conical Radon transform modelling Compton camera data. The formula exploits a large proportion of the acquired events and is easy to implement into fast algorithms. We give for it two equivalent formulations relying on known properties of the two-dimensional Radon transform and we test a semi-iterative algorithm for one of them. From a practical point of view, methods robust to measurement noise and to low number of events are required. We show that adding a constraint on the total variation of the final image strongly improves the results. We illustrate our arguments with Monte-Carlo simulated data in both low and realistic noise configurations.

3-D Reconstruction Benchmark of a Compton Camera Against a Parallel-Hole Gamma Camera on Ideal Data

“…For the CC analytic algorithm more events were necessary. From 25 × 10 6 simulated events, only one half were usable as a valid Compton cone should not intersect the detector in more than one point, the apex (for details, see reference [45]). A number of 12.5 × 10 6 counts were then simulated for the Anger camera with limited angular coverage.…”

“…In this work, we applied the filtered backprojection algorithm developed for CC image reconstruction in [45]. It was shown in [31] that an infinitely large planar detector offers a complete geometry, and the source can be perfectly reconstructed even from only events corresponding to cones with axes perpendicular to that plane.…”

“…This binning reduces the precision on the data and the effect on the image can be remarkable. For instance, a systematic error of 2.5°on the axis inclination will alter the point spread function (PSF) as one moves far from the detector ( [45], Fig. 7).…”

“…Lately, methods accepting a much larger part of the data were developed ( [35], [36], [37], [38]). The conical Radon transform is born and is receiving much interest ( [39], [40], [41], [42], [43], [44], [45], [46]).…”

Compton imaging reconstruction methods: a comparative performance study of direct back-projection, SOE, a new Bayesian algorithm and a new Compton inversion method applied to real data with Caliste

“…Once the optimal solution is found, we apply a TVregularization [20], which is used in Compton imaging with other algorithms [21], in order to denoise the source space image by minimizing ‖∇ ‖ � .…”