Small sample learning based on probability-informed neural networks for SAR image segmentation

The paper introduces a probability-informed methodology for the segmentation of synthetic aperture radar (SAR) images in the case of small sample learning. It assumes that the amount of training data is limited to several hundred or thousand elements, which prevents the effective training of state-of-the-art neural network (NN) models. This is a typical problem for real SAR images whose characteristics depend significantly on the sensors used to produce them and cannot always be repeated within open available datasets. To solve this problem, we propose NN models called Probability-Informed Neural Networks (PrINNs). As part of our approach, we introduce the use of probability models as a source of additional features for data. Specifically, the training dataset is enriched by modeling the pixel brightness using a finite normal mixture. We prove that such an extension can reduce errors in the learning process theoretically. The resulting enriched dataset is segmented using attention-based convolutional NNs or visual transformers. Then, post-processing is implemented based on another probability model—quadtree, which is a special case of random Markov fields. As we have theoretically demonstrated, this part of PrINNs is analogous to the graph-convolutional NNs with fixed weights. Using open SAR images obtained by different radars (namely, Sentinel-1, Capella, ESAR and HRSID) with various types of underlying surfaces, the possibility of improving segmentation quality based on PrINNs is demonstrated. We tested various combinations of methods from the PrINNs architecture, and in all cases, the PrINN approach we proposed was superior to any other combination of these methods. From the point of view of the achieved accuracy metrics, the mean $$F_1$$ score increased up to $$19.24\%$$ , and the median $$F_1$$ score was improved up to $$9.57\%$$ . Some further architectural improvements to PrINNs are also discussed in the paper.