## 2 Literature Review
[33] studied the application of the Latent Low-Rank Representation (LatLRR) [34] to PT data and introduced the Latent Low-Rank Representation Thermography (LatLRRT). LatLRR decomposes the signal into three matrices representing the observed data, the unobserved data, and the sparse noise, respectively. Unlike approaches such as those proposed by [PERSON] et al. [20; 21] where the data \(X\) is assumed to be the addition of three matrices, i.e., \(X=L+S+N\), in LatLRR, the data are assumed to be a linear association of the matrices, i.e., \(X=XZ+LX+N\). [PERSON] et al., reported that due to the very high memory usage of this approach, nowadays, it is not suitable as a defect detection approach. Nonetheless, it was able to significantly enhanced the output of the state-of-the-art approaches. Another trend regarding the processing of PT data consists in using machine learning methods. [PERSON] et al. [35; 36] proposed Partial Least Square (PLS) regression to improve the general quality of the image sequences. During the regression step, the PLS algorithm can model both spatially and temporally the evolution of the signal. It was originally proposed as a denoising technique allowing synthetic data reconstruction in a manner similar to Thermographic Signal Reconstruction (TSR) [37; 38]. In [36] [PERSON] et al. observed that by removing the loadings that have the highest variance from the reconstruction step, it is possible to reconstruct a sequence that highlights the defects. Inspired by these works, [PERSON] et al. [12] investigated the use of a pair of Support Vector Machine (SVM) algorithms [39] to enhance defect contrast. The first algorithm computes a regression in the time domain, while the second computes a regression in the space domain. Then the output sequence is reconstructed from these regressions providing images with enhanced defect contrast. [PERSON] et al. [40] introduced the Orthogonal Locality Preserving Projection Thermography (OLPPT). This method uses manifold learning. The experiments showed that it outperforms PCT. [PERSON] et al. [41] also proposed manifold learning method. When [PERSON] et al. [40] used a PCA as preprocessing stage, [PERSON] et al. [41] used an isometric feature mapping. [PERSON] et al. [41] approach also presented a noticeable improvement compared with state-of-the-art dimensionality reduction approaches such as PCT. In this study, the authors also investigated other state-of-the-art methods regarding local preservation. [PERSON] et al. [41] pointed that their method outperforms the PCT and other local preserving methods. The same year, these authors investigated the usage of a spatial neighborhood manifold learning for defect detection [42]. [PERSON] et al. [43] investigated the possibility of using a pre-trained ImageNet architecture to accurately predict the rank matrix from a given thermal sequence. [PERSON] et al. [44] employed a stacked autoencoder to extract defects from thermal data. The goal of this study was to model non-linear high-dimensional relationship between training data and their label to find defects from raw thermal sequences. [PERSON] et al. obtained good results compared with state-of-the-art approaches. [PERSON] et al. [45] used deep learning algorithm to both detect the defects and predict their depth. This approach used two state-of-the-art deep learning algorithms. They used transfer learning in association with a small labeled dataset to adapt the state-of-the-art algorithm to PT data. The results proved that algorithms performed well in both tasks. [PERSON] et al. analyzed the application of Artificial Neural Networks (ANN) on PT using synthetic data and showed that ANN outperforms the dynamic thermal tomography (DTT) [46]. Later the same authors [47] extended their previous work by studied the performance of wavelet, PCA, and Artificial Neural Networks (ANN). In their last study, they explained that ANN worked better than other methods. [PERSON] et al. [48] also used ANN to perform defect detection.