Linear digital tomosynthesis consists in acquiring on a digital detector a few projections, at different view angles and for a linear X-ray source path. A simple shift and add process reconstructs planes parallel to the detector plane but with a low vertical resolution. To improve it, we propose to use Algebraic Reconstruction Technique (ART) and Half Quadratic Regularization (HQR) methods, which are based on an iterative process. In such a linear digital tomosynthesis context, we propose to reconstruct independent 2D tilted planes passing through the linear source trajectory. Thus, computation time is reduced and it becomes possible to regularize in an anisotropic way to adapt the regularization process to the reconstructed volume sampling. We validate our approach with experimental data acquired on a digital detector. ART significantly improves the vertical resolution in comparison with usual process. However, ART is sensitive to noisy projections and may produce poor quality reconstructions. The HQR piecewise smoothness constraint stabilizes the reconstruction process. With a total angular range of 40 degrees, we can reach a vertical resolution lower than 1 cm, while it is superior to 3 cm with the usual process. Furthermore, HQR method significantly reduces truncation artifacts due to high projection angles.