Defects in magnetizable materials can be detected and evaluated by measuring electromagnetic data. The evaluation of this data relies on effective denoising techniques. In this talk, two types of denoising techniques for two different types of noise are presented. The first is based on wavelets and uses the stochastic denoising procedure of Donoho and Johnstone, the second one is based on curvelets and nonlinear approximation. Examples will be provided to demonstrate the issues involved and to validate the algorithms.