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In the magnetic flux leakage (MFL) method of nondestructive testing commonly used to inspect ferromagnetic materials, a crucial problem is signal inversion, wherein the defect profiles must be recovered from measured signals. This paper proposes a neural-network-based inversion algorithm to solve the problem. Neural networks (radial-basis function and wavelet-basis function) are first trained to approximate the mapping from the signal to the defect space. The trained networks are then used iteratively in the algorithm to estimate the profile, given the measurement signal. The paper presents the results of applying the algorithm to simulated MFL data.