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This article explores the Monotonicity Principle Method (MPM) for defect imaging in eddy current testing problems. This method determines if a voxel of the specimen is part of the defect or not by a simple test concerning the time constants of the source free response of an eddy current testing experiment. These simple tests comprise comparison operations thus resulting in a computational cost increasing as O(n),n being the number of unknown voxels. Therefore, this method is very low-cost in computation and provides real-time imaging capabilities. In practice, the performance of this method is highly limited by the accuracy of time constants, which have to be estimated from the transient waveform of a pulsed eddy current testing experiment. This contribution presents the first effort in estimating the time constants in the framework of MPM for pulsed eddy current testing: a method based on the Laplace-Padé approximant approach is proposed and validated through numerical examples.