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Robust estimation of diffusion models in presence of local artefacts that corrupt only a subset of gradient directions is essential in diffusion weighted imaging to accurately assess the brain connectivity and white-matter characteristics. In this work we investigate the estimation of diffusion tensors in the Random Sample Consensus (RANSAC) paradigm. First, we show that it enables robust estimation to artefacts such as patient motion during the images' acquisition and local signal loss due to the vibration artefact. Second, it provides us with a set containing only the reliable gradient directions at each voxel. This may enable robust but computationally efficient estimation of more complicated diffusion models by considering only the gradient directions identified as reliable at each voxel from the RANSAC tensor estimation.