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This article presents deep unfolding neural networks to handle inverse problems in photothermal radiometry enabling super-resolution (SR) imaging. The photothermal SR approach is a well-known technique to overcome the spatial resolution limitation in photothermal imaging by extracting high-frequency spatial components based on the deconvolution with the thermal point spread function (PSF). However, stable deconvolution can only be achieved by using the sparse structure of defect patterns, which often requires tedious, handcrafted tuning of hyperparameters and results in computationally intensive algorithms. On this account, this article proposes Photothermal-SR-Net, which performs deconvolution by deep unfolding considering the underlying physics. Since defects appear sparsely in materials, our approach includes trained block-sparsity thresholding in each convolutional layer. This enables to super-resolve 2-D thermal images for nondestructive testing (NDT) with a substantially improved convergence rate compared to classic approaches. The performance of the proposed approach is evaluated on various deep unfolding and thresholding approaches. Furthermore, we explored how to increase the reconstruction quality and the computational performance. Thereby, it was found that the computing time for creating high-resolution images could be significantly reduced without decreasing the reconstruction quality by using pixel binning as a preprocessing step.
The paper presents a numerical method to detect and characterise defects and inhomogeneities by means of active thermography. The objective was to determine the wall thickness of structure elements with an inaccessible back wall, e.g., elements of pipes or containers. As test specimens we used PVC samples with the thickness of about 2 cm that had spatial variations in the back wall geometry. Flash lamps provided the heating. To measure the thickness of the wall, we employed the LevenbergMarquardt method, which we applied here to experimental thermographic data for non-destructive testing. We started the inversion procedure by making a rough first estimation of the back wall geometry following the echo defect shape method, and then we calculated the thickness of the back wall. We found reasonable reconstruction results which differed from the real value significantly below 1 mm at the defect centre, whereas the error wais increased at the edge of the defect, depending on its shape and depth.