Fractal-domain deep learning with Transformer architecture for SAR ship classification

This paper extends deep learning from spatiotemporal-frequency to the fractal domain, and to the best of our knowledge, introduces for the first time the concept of fractal domain deep learning. Firstly, a Fractal Domain Transformer (FracFormer) model architecture is proposed to address the challenging problem of SAR image target classification in complex scenarios. Based on the Singularity Exponent-Domain Image Feature Transform (SIFT), FracFormer transforms original images into the fractal-domain feature images, utilizes fractal feature filters and combiners for iterative learning, and ultimately achieves image classification through fractal feature mixers and classifiers. Particularly, we derived the fractal feature filtering theorem based on SIFT and the feature combination theorem based on SIFT, providing theoretical support for the design of the core modules of FracFormer. On the OpenSARShip2.0 dataset, our model outperforms baseline models, with improvements ranging from 0.37 % to 11.83 % on average. Besides, extensive visualization analysis of the model’s fractal domain feature learning results indicates that FracFormer accords with the two theorems, representing good interpretability. Furthermore, FracFormer demonstrates fast convergence and strong generalization in low signal-to-noise ratio scenarios. Specifically, at 0 dB sea clutter, it achieves a 9.96 % improvement in classification performance over frequency domain GFNet and accelerates convergence by approximately 36 %. The findings of this study are expected to provide new learning paradigms and model architectures for the fields of deep learning and computer vision.