This study develops a methodology for determining the absolute permeability distribution in a porous media sample using velocity data obtained from NMR imaging experiments. An objective function describing the discrepancy between observed and simulated data is reduced by iteratively updating the permeability. This parameter estimation scheme is based on an iterative method which uses optimal control theory to refine the estimates. Although this theory is developed for both isotropic and anisotropic porous media, the permeability reconstructions examined in this paper are restricted to the isotropic case. Synthetic data are used to investigate the impact of varying the noise in the experimental data, the degree of parameterization, the relative weighting of the regularization term in the objective function, and the amount and type of data required to obtain a satisfactory permeability reconstruction. These synthetic data are extracted from the solution of numerical experiments that have utilized an assumed permeability distribution. The methodology is also applied to data gathered in laboratory experiments for water flow in a sandstone sample.