  This paper presents deep unfolding neural networks to handle inverse problems
in photothermal radiometry enabling super resolution (SR) imaging. Photothermal
imaging is a well-known technique in active thermography for nondestructive
inspection of defects in materials such as metals or composites. A grand
challenge of active thermography is to overcome the spatial resolution
limitation imposed by heat diffusion in order to accurately resolve each
defect. The photothermal SR approach enables to extract high-frequency spatial
components based on the deconvolution with the thermal point spread function.
However, stable deconvolution can only be achieved by using the sparse
structure of defect patterns, which often requires tedious, hand-crafted tuning
of hyperparameters and results in computationally intensive algorithms. On this
account, Photothermal-SR-Net is proposed in this paper, which performs
deconvolution by deep unfolding considering the underlying physics. This
enables to super resolve 2D thermal images for nondestructive testing with a
substantially improved convergence rate. Since defects appear sparsely in
materials, Photothermal-SR-Net applies trained block-sparsity thresholding to
the acquired thermal images in each convolutional layer. The performance of the
proposed approach is evaluated and discussed using various deep unfolding and
thresholding approaches applied to 2D thermal images. Subsequently, studies are
conducted on how to increase the reconstruction quality and the computational
performance of Photothermal-SR-Net is evaluated. 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.
