A novel optimization-based method for pole figure inversion is presented within the framework of finite elements over Rodrigues parameter space. A model orientation distribution function (ODF) is used to assess the performance of the method as compared to similar implementations of the basic WIMV algorithm and the maximum entropy method. The new method, coined the hybrid H-1-seminorm minimization, provides a conditional ghost correction that is much less sensitive to the orientation space discretization than the other methods. It is also shown to reconstruct the model ODF most accurately when random noise is applied to the input pole figure data.