## 2 Literature Review  
As previously mentioned, the sensibility of a thermal camera to noises makes the field of PT eager for new processing methods. In this section, we briefly introduce some of the most recent work. Inspired by the work of [PERSON] et al., known as PPT, [PERSON] et al., investigated a feature base approach based on monogenic signal reconstruction for defect detection. Although the approach happened to be highly sensitive to noise, promising results were found. More recently, [PERSON] et al. [16] proposed two reformulations of the PPT, which improve the Contrast-to-Noise Ratio (CNR). [PERSON] et al. [17] proposed a phase and time-domain tomography for defecting defects in composite materials. [PERSON] et al. [18] introduced an adaptive spectral processing. The method is more robust than the PPT, offers a better SNR even for barely visible defects. It also returns a single index map of the defects for a given sequence which makes it easier to interpret. Another popular trend regarding the methods used to process PT data is the application of linear-algebra methods. [PERSON] et al. [13] introduced an approach that consists of associating a sparse matrix factorization with a Mixture of Gaussian (MoG). The enhancement of the data is based on the sparse matrix factorization, which is solved as a minimization problem, in which the noise of the data is modeled by an MoG. The authors chose to model the noise in the data as an MoG due to its better reliability to the real case than traditional approaches that assume that the noise follows one model such as Gaussian or Laplacian. Later, the same authors introduced a wavelet-based approach in order to enhance the defect present in an image [19]. The same year they use this approach with a minimization approach, allowing them to separate a low-rank matrix, a sparse matrix, and a noise matrix from the data. They showed that this approach is state-of-the-art approaches [20]. Recently [PERSON] et al. introduced another sparse low-rank optimization approach [21]. In this work, [PERSON] et al. reuse the three matrix decomposition they already used in [20], but this time they introduced an activation function based on the immediate past in the cost function. Inspired by the work of [PERSON] et al., [PERSON] et al. [22] proposed an alternating sparse matrix decomposition. Like in the work of [PERSON] et al., [PERSON] et al., assumed that the data are the summation of three matrices, respectively a low-rank, a sparse, and the noise. They extend previous works by assuming that the sparse matrix is the product of a dictionary matrix with a matrix of weights. The goal of this assumption regarding the sparse matrix is to better model the background noises. [PERSON] et al. [23] introduced the Candid-Covariance Free Principal Component Thermography (CCIPTCT). CCIPT is based on the work of [PERSON] et al. [24] who has introduced the Candid-Covariance Free Principal Component Analysis (CCIPCA). [PERSON] et al. [25] introduced the SPCT, an application of the Sparse-PCA to PT. They showed that SPCT outperformed existing methods at a noticeably higher computational cost. The Sparse-PCA is a formulation of the PCA as a penalized regression problem under constraints. One year before [PERSON] et al., [PERSON] et al. [26] proposed a two-step approach based on Sparse-PCA as the first step, refined by kernel-k-means during the second step. In this study, [PERSON] et al. focused on the robustness of their method to noise. [PERSON] et al. [27; 28] used an improved version of the Sparse-PCA named the Edge-Group Sparse PCA (ESPCT), which is able to preserve the spatial connectivity [29]. They showed on experiments conducted on CFRP samples, that ESPCT results offer a higher contrast on smaller defects. Recently [PERSON] et al. studied several Non-negative Matrix Factorization (NMF) methods [30; 31; 32]. These studies showed that NMF approaches offer noticeably better performance than other component-based approaches regarding the defects detection on CFRP. [PERSON] et al.