Eecient Sampling on Coarse Grids in Tomography List of Figures

In tomography we have to give an estimate of a function from a nite number of its intergrals along straight lines or on strips. Under very reasonable conditions, the interlaced sampling is well known to be the most eecient scheme for this problem. In this paper we examine some pertu-bations on the interlaced scheme. Using a theorem due to A. Faridani, we show that sampling on coarse grids leads to eecient schemes, allowing to consider a lot of diierent sampling geometries. Some of them could be in practice much more easily generated than the interlaced one. New eecient sampling schemes of the Radon transform are proposed. Numerical experiments in the case of integrals on strips show the eeciency of these new schemes. 1 Measurement strips scheme in the original interlaced sampling proposed by Cormack for odd and even directions. 3 A new parallel scanning geometry with the use of two detectors. On the left: three successive positions of the sources (small rectangle) with the two measured beam (the detectors are supposed to be on the end but are not represented). The system source+2 detectors is just translated. This permits to scan the direction and +. On the right: the Radon transform sampling points in the (;) space. This sampling points are almost interlaced: a perturbation of a factor cos(