## 4 Materials and Methods
### Analysis  
In this study, we investigated different aspects regarding the usage of the Independent Component Analysis. We chose to compare the results of our experiments with two state-of-the-art methods, the PPT [8], and the PCT [9]. We conducted three investigations regarding the importance of selecting the component on the accuracy of the results, evaluating the different methods we selected, and finally, the influence of the acquisition frequency on our data's accuracy. The first aspect of our study concerns the selection of the number of components. Several papers have been published offering methods regarding selecting the number of components regarding different applications optimally. Although the work of [PERSON] et al. [119] fits our goals, they used a nonquadratic activation function given in Equation (10) and developed a method to identify the most suitable independent component for detecting defects. However, this method can not be generalized for other activation functions; thus, we chose not to use it in our study. Therefore we conducted a limited study regarding the importance of selecting the proper number of components for ICA. For each method under investigation and each dataset, we reduced the dimensionality to one hundred and seven components. The numbers seven and one hundred were randomly selected. We compute the CNR for both cases and every defect. Then the results for seven and one hundred components are compared.  
Then for a given defect we identify the frame with the highest CNR score, which we report in our results. For each defect, the CNR is computed for a region of interest representing the defective region and a region of interest used as a sound area, as one can note in Figure 4. One can note that the sound area overlaps the defective region, it is obvious that for the computation of the CNR all overlapping pixels were not considered part of the sound area. For evaluation of all selected methods, we use CNR values of seven components. For the PPT the CNR values were computed the same manner as those of the ICA's methods. Figure 5 shows the different step of our experiment. Another aspect of the evaluation of the different methods concerns their ability, when coming to the segmentation task, is to provide an accurate mask of the defects present in the sample. Inspired by [PERSON] et al. [72], to construct a single image from the several components or phase images, we compute the InterQuartile Range (IQR) for each pixel of selected outputs. Then, from this image, we used the triangle automatic threshold method [124] to compute an optimal threshold, which is applied to the previous image to generate a mask of the defects. We thus estimated the accuracy based on these images and compare it with other methods. Figure 6 shows the different steps of this experiment. To conclude our study we compare the results we computed from each method between the different acquisition frequencies.  
Figure 4: The blue contour represents the defect region, while the region between the green an red contours is our sound area.  
Before any analysis, we first need to pre-process the sequence we acquired. We acquired a sequence of \(T\) images of \(M\times N\) pixels that are structured as a third-order tensor for each frequency. The first step consists in creating an overlay matrix of dimension \(T\times P\) where \(P=M.N\). \(T\) is the number of frames acquired in each sequence, \(P\) is the total number of pixels. Figure 7 shows that operation.  
Figure 5: Research block diagram.  
Figure 6: Segmentation and accuracy computation flow diagram.  
Figure 7: Transformation of acquisition from a third-order tensor to a matrix.  
As preprocessing we standardized the overlay matrix. To do so we compute the mean and standard deviation of each column of the matrix, thus for each row of the matrix we subtract the mean vector previously computed and divide it by the standard deviation vector. In the next section, we introduce the metrics we use for assessing the quality of the different methods we investigated.