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The Compton camera is an imaging device relevant for the detection of prompt photons produced during nuclear fragmentation in hadrontherapy. It allows a considerable improvement in detection compared to a standard gamma-camera but also requires more sophisticated image reconstruction techniques. In this work we apply a recently developed filtered backprojection algorithm to data simulated from a realistic Compton camera prototype designed for hadrontherapy on-line monitoring. We reconstruct images of a point source having a broad energy spectrum compatible with the up-mentioned application. Preliminary results indicate that the achievable resolution in directions parallel to the camera, thus including the beam direction, are compatible with the quality control requirements. With the prototype under study, the reconstructed image is elongated in the direction orthogonal to the camera. However this direction is of less interest and the resolution may be easily recovered using a second camera.