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Learned block iterative shrinkage thresholding algorithm for photothermal super resolution imaging
(2022)
Block-sparse regularization is already well known in active thermal imaging and is used for multiple-measurement-based inverse problems. The main bottleneck of this method is the choice of regularization parameters which differs for each experiment. We show the benefits of using a learned block iterative shrinkage thresholding algorithm (LBISTA) that is able to learn the choice of regularization parameters, without the need to manually select them. In addition, LBISTA enables the determination of a suitable weight matrix to solve the underlying inverse problem. Therefore, in this paper we present LBISTA and compare it with state-of-the-art block iterative shrinkage thresholding using synthetically generated and experimental test data from active thermography for defect reconstruction. Our results show that the use of the learned block-sparse optimization approach provides smaller normalized mean square errors for a small fixed number of iterations. Thus, this allows us to improve the convergence speed and only needs a few iterations to generate accurate defect reconstruction in photothermal super-resolution imaging.
Thermographic photothermal super resolution reconstruction enables the resolution of internal defects/inhomogeneities below the classical limit, which is governed by the diffusion properties of thermal wave propagation. Based on a combination of the application of special sampling strategies and a subsequent numerical optimization step in post-processing, thermographic super resolution has already proven to be superior to standard thermographic methods in the detection of one-dimensional defect/inhomogeneity structures. In our work, we report an extension of the capabilities of the method for efficient detection and resolution of defect cross sections with fully two-dimensional structured laser-based heating. The reconstruction is carried out using one of two different algorithms that are proposed within this work. Both algorithms utilize the combination of several coherent measurements using convex optimization and exploit the sparse nature of defects/inhomogeneities as is typical for most nondestructive testing scenarios. Finally, the performance of each algorithm is rated on reconstruction quality and algorithmic complexity. The presented experimental approach is based on repeated spatially structured heating by a high power laser. As a result, a two-dimensional sparse defect/inhomogeneity map can be obtained. In addition, the obtained results are compared with those of conventional thermographic inspection methods that make use of homogeneous illumination. Due to the sparse nature of the reconstructed defect/inhomogeneity map, this comparison is performed qualitatively.