Multi-Scale Graph Wavelet Convolutional Transformer for HSI-LiDAR Data Fusion and Classification

Hyperspectral images (HSIs) and LiDAR data are frequently employed conjointly for land-cover mapping due to the unique advantages each provides. HSIs offer comprehensive spectral information at the pixel level, facilitating the identification of materials that appear similar in conventional imagery. Conversely, LiDAR supplies precise elevation and three-dimensional structural data, which remains unaffected by variations in lighting conditions. Nonetheless, integrating these modalities remains challenging due to the "over-smoothing" phenomenon in Deep Graph Neural Networks (GNNs), which blurs local class boundaries, and the inability of local Convolutional Neural Networks (CNNs) to capture long-range semantic dependencies. Furthermore, these challenges are exacerbated when labeled training samples are scarce. To address these issues, we propose the Multi-Scale Graph Wavelet Convolutional Transformer (MS-GWCT), a novel methodology for fusing and classifying HSI and LiDAR data. Unlike standard GNNs, MS-GWCT constructs a spatial graph at the pixel scale, connecting labeled samples and capturing both fine-grained and broad spectral-spatial patterns through multi-scale graph wavelet convolutions. MS-GWCT employs a learnable Chebyshev wavelet filter to retain high-frequency signal components (edges and fine details) while filtering noise. To capture global context, a graph Transformer module with multi-head self-attention aggregates information across distant nodes. We further enhance robustness in limited-label scenarios via a Schrödinger Optimization Algorithm (SOA) for hyperparameter search and a supervised contrastive loss. We evaluated MS-GWCT on the Houston 2013 and Trento benchmarks, adhering to the standard protocol of 50 samples per class, and compared its performance with that of leading HSI-LiDAR fusion methodologies. Our approach achieved overall accuracies of 92.60% on Houston 2013 and 98.86% on Trento, surpassing alternative techniques. Additional ablation studies confirm the significance of both the multi-scale graph wavelet convolution and the graph Transformer attention module in attaining these outstanding results.