Imaging processes built on the Compton scattering effect are currently under intense investigation. However, despite many innovative contributions, this topic still pose a formidable mathematical and technical challenge. In this work, we argue that, in the framework of single-photon emission imaging, collecting Compton scattered radiation from an emitting object, allows to image the radiotracer distribution in vivo. Data is acquired by a stationary collimated gamma camera under the form of compounded conical projections of the activity density function. Mathematically, the image formation process is described by the so-called Compounded Conical Radon Transform (CCRT) and three-dimensional object reconstruction is based on an inversion formula of the CCRT. We perform numerical simulations to show the feasibility of this new imaging modality, which offers the remarkable advantage of operating in stationary mode without the need of bulky and cumbersome spatial rotational mechanism of conventional gamma cameras. This is highly attractive for applications in medical imaging, industrial non-destructive evaluation, nuclear waste storage surveillance and homeland security monitoring. Finally, to improve drastically the sensitivity, we introduce a new feature allowing to acquire data without mechanical collimation and support the findings with some preliminary simulation results.