  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. To avoid time-consuming manually selected
regularization parameter, we propose a learned block-sparse optimization
approach using an iterative algorithm unfolded into a deep neural network. More
precisely, we show the benefits of using a learned block iterative shrinkage
thresholding algorithm that is able to learn the choice of regularization
parameters. In addition, this algorithm enables the determination of a suitable
weight matrix to solve the underlying inverse problem. Therefore, in this paper
we present the algorithm and compare it with state of the art block iterative
shrinkage thresholding using synthetically generated test data 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 than
without learning. Thus, this new approach allows to improve the convergence
speed and only needs a few iterations to generate accurate defect
reconstruction in photothermal super resolution imaging.
