Abstract: In order to carry out a three-dimensional reconstruction of an object acquired by a series of conical projections on a two-dimensional multidetector, the object is estimated by a sampled function. The sampled function is projected and the projections of the sampled function are compared with the measurements resulting from acquisition on the 2D multidetector. A new estimation of the object is deduced therefrom and these operations are repeated until the comparison is satisfactory. In order to project, the sampled three-dimensional object is decomposed on a space of Gaussian basis functions. The contribution of the basis functions is computed for each image of the projection images, these contributions being equal to the integral of the product of the basis functions and of a support for illumination of the image element.