Adapted sampling for 3D X-ray computed tomography

In this paper, we introduce a method to build an adapted mesh representation of a 3D object for X-Ray tomography reconstruction. Using this representation, we provide means to reduce the computational cost of reconstruction by way of iterative algorithms. The adapted sampling of the reconstruction space is directly obtained from the projection dataset and prior to any reconstruction. It is built following two stages : firstly, 2D structural information is extracted from the projection images and is secondly merged in 3D to obtain a 3D pointcloud sampling the interfaces of the object. A relevant mesh is then built from this cloud by way of tetrahedralization. Critical parameters selections have been automatized through a statistical framework, thus avoiding dependence on users expertise. Applying this approach on geometrical shapes and on a 3D Shepp-Logan phantom, we show the relevance of such a sampling - obtained in a few seconds - and the drastic decrease in cells number to be estimated during reconstruction when compared to the usual regular voxel lattice. A first iterative reconstruction of the Shepp-Logan using this kind of sampling shows the relevant advantages in terms of low dose or sparse acquisition sampling contexts. The method can also prove useful for other applications such as finite element method computations.