Abstract This study presents the development of a spatially adaptive weighting strategy for Total Variation regularization, aimed at addressing under-determined linear inverse problems. The method relies on the rapid computation of an accurate approximation of the true image (or its gradient magnitude) through a neural network. Our approach operates without requiring prior knowledge of the noise intensity in the data and avoids the iterative recomputation of weights. Additionally, the paper includes a theoretical analysis of the proposed method, establishing its validity as a regularization approach. This framework integrates advanced neural network capabilities within a regularization context, thereby making the results of the networks interpretable. The results are promising as they enable high-quality reconstructions from limited-view tomographic measurements.
Morotti et al. (Mon,) studied this question.