Table 3.

Summary of signal processing techniques used for OST.

Signal Processing Method	Abbreviation		Basic Principle
Differential Absolute Contrast [42,43]	DAC		It is one of the well-known processing technique that uses the difference between the temperature of a sound area and a defected area. DAC is based on the 1D solution of the Fourier heat equation.
Thermographic Signal Reconstruction [44,45]	TSR		It creates polynomial filters from log-log pre-calculations for the surface temperature response on each pixel by fitting a low-order polynomial function to the temperature evolution cooling profiles. Basic TSR significantly reduces the noise in thermal images and it can be used to generate time-derivative images without additional noise contribution. These time-derivative images can reduce the effects of non-uniform heating, the background reflection artefacts and provide good sensitivity to smaller and deeper defects. However, TSR only filters data temporally and does not make use of the spatial information.
Principal Component Thermography [46]	PCT		It uses the singular value decomposition (SVD) method to reduce an appropriately constructed matrix of observations to a set of orthogonal functions that produce a useful representation of both spatial information and temporal features for pulse thermography images. This technique provides an estimate of the average flaw depth within a flawed zone but does not provide any indication of the damage distribution. PCT is also computationally expensive.
Correlation Extraction Algorithm [47]		CEA	It is widely used in lock-in thermography and it is based on the principle that the harmonic thermal response measured by the IR camera is analysed with in-phase correlation and cross-correlation functions in order to extract information about the amplitude and phase of measured thermal signals. The feasibility of this technique depends on the length of the image sequence.
3D Normalisation Algorithm [48]		3DNA	It suppresses surface clutter conditioned by uneven heating and lateral heat diffusion for pulsed thermography. The algorithm does not require selecting a reference point for the sound area and involves the division of the IR image sequence in synthetic sequences, which are calculated by solving the corresponding three-dimensional problem of heat conduction. This method requires the determination of material thermal properties.
Multi-dimensional Ensemble Empirical Mode Decomposition [49]		MEEMD	It is used to decompose the TSR-smoothed thermal image into the high-frequency noise, low-frequency background and the informative part of the signal in order to remove the noise and non-uniform background from the thermographic data, thus improving the damage detection capabilities.
Gapped Smoothing Algorithm [50]		GSA	It is a two-dimensional reference-free quantitative detection method for sub-surface defects used for pulsed thermography. It relies on the determination of a damage index pattern that is function of the thermal contrast between real and estimated temperature profiles for all pixels. GSA method can enhance the thermal contrast and suppress the effect of non-uniform heating. It was also shown to improve the detection of damage far from the heating surface.
Partial Least Squares Thermography [51]		PLST	It is mainly used for pulsed thermography and it is based on the partial least squares regression (also known as projection to latent structures) that computes new thermal sequences that are correlated to the predicted block Y and the predictor matrix X. The matrix X corresponds to the surface temperature matrix obtained during the thermography inspection, whilst Y is defined by the observation time during which thermal images are captured. The new set of thermal images and observation time vector is composed of variables that consider only the most important signal variations. Unnecessary information present in the original thermal sequence is neglected. Contrary to PCT, PLST keeps track of the time. Hence data set can be decomposed, manipulated and recomposed, for example by omitting certain loadings with as benefits enhanced signal-to-noise ratio (SNR).
Coefficient Clustering Analysis [52]		CSA	It is a reference-based quantitative detection method based on fitting a second order polynomial model for temperature decay curves. The coefficients of the model are much less sensitive to noise and more consistent for pixels from the sound area as compared to a high order model. This technique not only provides an enhanced visual confirmation of the damage, but it also reduces the burden on the operator in post-processing data.