[en] 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. (paper)