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The two‐dimensional phase unwrapping problem is studied. Using the minimum L^p‐norm approach, we apply three different non‐linear multigrid algorithms for reconstructing surfaces from their ‘wrapped’ values—two classical approaches and a novel multilevel non‐linear method (MNM). The methods prove to be efficient even for difficult problems with noisy and discontinuous original images. The new method, MNM, exhibits the fastest and most robust convergence of the three, given an appropriate choice of a damping parameter. This parameter is determined automatically on very coarse grids at a small computational cost. Copyright 2004 John Wiley & Sons, Ltd.