An adapted fan volume sampling scheme for 3D algebraic reconstruction in linear tomosynthesis

We study the reconstruction process when the X-ray source translates along a finite straight line, the detector moving or not. This process called linear tomosynthesis induces a limited angle of view which causes the vertical spatial resolution to be poor. To improve this resolution we use iterative algebraic reconstruction methods which are commonly used for tomographic reconstruction from a few number of projections. With noisy projections, such algorithms produce poor quality reconstructions. To prevent this, we use a first object prior knowledge consisting in piecewise smoothness. To reduce the computation time associated with both reconstruction and regularization processes, we introduce a second geometrical prior knowledge based on the linear trajectory of the X-ray source. This linear source trajectory allows us to reconstruct a series of 2D planes in a fan organization of the volume. Using this Adapted Fan Volume Sampling Scheme, we reduce the computation time by transforming the initial 3D problem into a series of 2D problems. Obviously the algorithm becomes directly parallelizable. Focusing on a particular region of interest becomes easier too. The regularization process can easily be implemented with this scheme. We test the algorithm using experimental projections. Quality of the reconstructed object is conserved while the computation time is considerably reduced even without any parallelization of the algorithm.