Mojette reconstruction from noisy projections

Abstract

Apart from the usual methods based on the Radon theorem, the Mojette transform proposes a specific algorithm called Corner Based Inversion (CBI) to reconstruct an image from its projections. Contrary to other transforms, it offers two interesting properties. First, the acquisition follows discrete image geometry and resolves the well-known irregular sampling problem. Second, it updates projection values during the reconstruction such that the sinogram contains only data for not yet reconstructed pixels. Unfortunately, the CBI algorithm is noise sensitive and reconstruction from corrupted data fails. In this paper, we develop a new noise-robust CBI algorithm based on data redundancy and noise modelling in the projections. This algorithm is applied in discrete tomography from a Radon acquisition. Reconstructed image results are discussed and applications in usual tomography are detailed.