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Using x-ray magnetic nanotomography the internal magnetization structure within extended samples can be determined with high spatial resolution and element specificity, without the need for assumptions or prior knowledge of the magnetic properties of a sample. Here we present the details of a new algorithm for the reconstruction of a three-dimensional magnetization vector field, discussing both the mathematical description of the problem, and details of the gradient-based iterativedoi:10.1088/1367-2630/aad35a fatcat:2cppaypd4fbfhcv43szhny3rjq