With the increasing use of induction thermography (IT) for non-destructive testing (NDT) in the mechanical and rail industry, it becomes necessary for the manufactures to rapidly and accurately monitor the health of specimens. The most general problem for IT detection is due to strong noise interference. In order to counter it, general post-processing is carried out. However, due to the more complex nature of noise and irregular shape specimens, this task becomes difficult and challenging. In this paper, a low-rank tensor with a sparse mixture of Gaussian (MoG) (LRTSMoG) decomposition algorithm for natural crack detection is proposed. The proposed algorithm models jointly the low rank tensor and sparse pattern by using a tensor decomposition framework. In particular, the weak natural crack information can be extracted from strong noise. Low-rank tensor based iterative sparse MoG noise modeling is carried out to enhance the weak natural crack information as well as reducing the computational cost. In order to show the robustness and efficacy of the model, experiments are conducted for natural crack detection on a variety of specimens. A comparative analysis is presented with general tensor decomposition algorithms. The algorithms are evaluated quantitatively based on signal-to-noise-ratio (SNR) along with the visual comparative analysis.