In this paper, we propose novel inversion methods to estimate defects or localized current anomalies in membrane electrode assemblies (MEAs) in polymer electrolyte fuel cells (PEFCs). One method is an imaging approach with L1-norm regularization that is suitable for estimation of focal anomalies compared to Tikhonov regularization. The second is a complex analysis based method in which multiple pointwise current anomalies can be identified directly and algebraically from the measured magnetic flux density.