D3A-Net: A Deformable 3-D Attention Network for Hyperspectral Unmixing

Abstract

Hyperspectral unmixing (HU) aims to decompose mixed pixels into endmember spectra and corresponding abundance maps under physically interpretable constraints. Despite recent progress in convolutional neural network (CNN)- and Transformer-based approaches, most existing methods still rely on rigid sampling grids or process spatial and spectral features separately, which may cause feature misalignment for irregular and elongated structures and weaken spectral–spatial volumetric continuity. To address these limitations, we propose a deformable 3-D attention network (D3A-Net), a fully 3-D U-shaped encoder–decoder that processes hyperspectral imagery as a unified data cube and overcomes the constraints of fixed receptive fields. D3A-Net is constructed by stacking 3D-DeFormer blocks (3D-DFBs), each of which incorporates a 3-D multiscale deformable neighbourhood-attention (MS-DNA) module and a complementary local extraction branch, followed by a gated feed-forward module for efficient feature transformation. The physics-guided unmixing Encoder II enforces the abundance nonnegativity and sum-to-one constraints, while the linear decoder reconstructs the hyperspectral image (HSI), enabling end-to-end unsupervised learning. Extensive experiments on a synthetic dataset under multiple signal-to-noise ratio (SNR) settings and three real-world datasets (Samson, Jasper Ridge, and APEX) demonstrate that D3A-Net achieves accurate endmember estimation and abundance estimation.