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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. These properties could be a solution to reduce the missing wedge effect in tomography. Unfortunately, the CBI algorithm is noise sensitive and reconstruction from corrupted data fails. In this paper, we first develop and optimize a noise-robust CBI algorithm based on data redundancy and noise modelling in the projections. Afterwards, this algorithm is applied in discrete tomography from a specific Radon acquisition. Reconstructed image results are discussed and applications and perspectives to reduce the missing wedge effect are also developed.