## 4 Image Fusion Applications in NDT Inspection
### Wavelet-Based Approaches  
The wavelet transform is an appropriate tool to decompose images into high- and low-frequency components. This makes possible analysis of the features of data over a certain scale, such as the edges and texture for an image or the frequency for a signal. Unlike the Fourier transform, which offers a specific frequency wave, it can provide data \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sources** & **Material** & **Defect Types** & **Aim** & **Reference** \\ \hline Lock-in thermography & GFR composite & Foreign body or & To eliminate non-uniform & \\  & & delamination & heating, low resolution & [66] \\  & & & and noise effects & \\ \hline Ultrasonic and & & Holes with different & To detect holes and & \\ vibro-acoustographic inspection & Steel pipe & shapes & measure their dimensions & [21] \\ \hline Eddy current pulse & Aluminum alloy or & & & \\ thermography & stainless steel & Crack & To eliminate background & \\  & & stainless steel & interference effect & [68] \\ \hline Thermal and & & & & \\ visible images & Steel & Crack or split & To solve heat diffusion, & \\  & & & reflection and illumination & \\  & & & problems of constituent & \\  & & & methods & \\ \hline Pulsed thermography & GFR composite & Foreign body or & To enhance the defect & \\  & & delamination & detection capability & [45] \\ \hline Lock-in thermography & SS275 steel plate & Voids or corrosion & To inspect the contaminant & \\  & & & liner plate (CLP) against & \\  & & & radiation leakage & \\ \hline Lock-in thermography & CFRP composites & Holes & To find better depth & [67] \\  & & & resolution & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: A list of PCA-based studies for NDT image fusion. representation for multiple scales with different versions of wavelets. Shifted and scaled versions of a wavelet can positively impact the resolution in the time or frequency domain according to the selected parameters. The wavelet transform aims to maintain a good resolution in the time and frequency domain, contrary to the Fourier transform [73; 74]. For an image, the row and column directions must be handled independently when the original image is divided into four sub-band images. The two-level decomposition structure is illustrated in Figure 5 for illustration purposes. Each row's data are first used to utilise the high-pass filter \(H\) and the low-pass filter \(L\), and then the high- and low-frequency components of the row are obtained by downsampling of the two. The next step is the same in the column base and continuous for the next decomposition levels iteratively. The low-pass portion (LL), called the approximation or wavelet coefficients, contains the average image information, and the high-pass portion (i.e., detail coefficients) has the directional information of the original image. By using this approach recursively, multi-resolution wavelet analysis can be performed [75]. The decomposition level and selection of the proper wavelet filter, one of the most important steps for wavelet application, should be decided according to the structure, aim of the transformation and the information that should be emphasised. The authors of [76] proposed a wavelet energy-based (\(E_{min}\)) filter selection method which considers that the minimum percentage of the approximation coefficients and detail coefficient will bring minimal noise. This is attributed to the minimum amount of low-frequency information in the approximation coefficient after decomposition. Additionally, a weighted risk factor-based decomposition, including automatic level selection, is used according to the maximum detail coefficients. The primary goal of the proposed strategy is to eliminate noise while maintaining appropriate defect information. The results show that the risk factor-based fusion provided more visual and qualitative detection than the minimum energy-based approach.