We introduce a new kind of radon transform, consisting in integrating a function (to be recovered) over a special family of cones. It is in fact a formal generalization of the "Coded-aperture gammagraphy" imaging method, encountered in medicine and astronomy. We show that it is a natural geometric operation, but which does not have the fine properties of similar integral transform. Nevertheless, several inverse problems (like classical radon transform, deconvolution) are related to it, and also new kinds on integral transforms : essentially the "Quasi-convolution". After this study, where we show that the problem is severely ill-posed (essentially because of insufficient data), an inversion is performed in the case of complete data.