Multi-task Disentangling Fusion Mamba-CNN for MODIS Spectral-Temporal Unmixing with Endmember Variability Modeling

Spectral-temporal unmixing of MODIS time series is essential for applications such as abundance mapping and spectral library construction, yet it remains challenging due to (i) spectral-temporal information coupling in MODIS data, (ii) intra-class endmember spectral variability and inter-class signature ambiguity, and (iii) the instability of naively fusing multiple expert representations. This paper presents the Multi- task Disentangling Fusion Mamba (MDF-Mamba) to address these limitations. To resolve spectral-temporal coupling, we design a disentangling architecture that pairs per-channel spectral experts with a dedicated bidirectional state-space (Mamba) temporal branch. Convolutional modules each process a single spectral channel, while the Mamba branch encodes the cross-channel seasonal trajectory, forming a multi-branch expert ensemble with soft inter-expert reweighting based on squeeze-and-excitation. For the integration of these spectral and temporal expert outputs, we introduce mHCFusion, adapting the manifold-constrained hyper-connection framework to merge the outputs in a stable and interpretable manner. Endmember variability is addressed by extending the linear mixing model with pixel-wise learnable spectral variability weights that capture intra-class endmember variation. Finally, we design a multi-task training objective that combines supervised abundance estimation with self-supervised spectral reconstruction and endmember regularization terms on the same training data, yielding a highly efficient framework for spectral-temporal unmixing. Experiments on MODIS time series covering the Alberta and Saskatchewan provinces show that MDF-Mamba achieves the best performance on 12 of 14 evaluation metrics across both datasets (7 of 7 on Alberta; 5 of 7 on Saskatchewan), ranking second on the remaining two.