Discrete signal transforms as a tool for processing and analyzing pulsed thermographic data

Abstract

In this paper, we review some of the discrete signal transforms that are in use in the field of thermography for defect detection and/or characterization. Signal transformation is used with the purpose of finding an alternative domain where data analysis is more straightforward. For instance, it is possible to pass from the time domain to the frequency spectra through the one-dimensional discrete Fourier transform (DFT). The DFT constitutes the basis of pulsed phase thermography (PPT), but other transformations are possible such as the discrete wavelet transform (DWT) with the advantage that, in this case, time information is preserved after the transformation. It is also possible to rearrange data into domains others than frequency. For instance, the Hough transform (HT) allows the detection of regular forms (e.g. lines, curves, etc.) in a parameter space. The HT has been used in two different ways in thermography: for the detection of lines in thermal profiles, with the goal of discriminating between defective and non-defective regions; or it can be used to locate the inflection points in phase profiles obtained by PPT to extract the blind frequencies. The Laplace transform can also be used in the time domain to improve flaws detection and their characterization in the transformed space. Eigenvector-based transforms, such as singular value decomposition (SVD), have also been implemented. Principal component thermography (PCT) uses SVD to decompose thermographic data into a set of orthogonal modes. We discuss all these transforms and provide some comparative results.