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This paper describes a new discrete method for inverting X‐ray pole figures to estimate the orientation distribution function (ODF). The method employs the equal‐volume `cubochoric' representation for uniform discretization of orientation space, SO(3). The forward‐projection model is combined with an anisotropic total variation term to iteratively determine the ODF. The efficacy of the new method is evaluated with both model and experimental data and compared with existing discrete and series expansion methods.