A Novel Sub-Abundance Map Regularized Sparse Unmixing Framework Based on Dynamic Abundance Subspace Awareness

Sparse unmixing (SU) has become a research hotspot in hyperspectral image (HSI) analysis in recent years due to its interpretable physical mechanisms and engineering practicality. However, traditional SU methods are confronted with two core bottlenecks: Firstly, the high computational complexity of the abundance matrix inversion severely limits algorithmic efficiency. Secondly, the inherent challenges posed by large-scale highly coherent spectral libraries hinder improvement of unmixing accuracy. To overcome these limitations, this study proposes a novel sub-abundance map regularized sparse unmixing (SARSU) framework based on dynamic abundances subspace awareness. Specifically, first of all, we have developed an intelligent spectral atom selection strategy that employs a designed dynamic activity evaluation mechanism to quantify the participation contribution of spectral library atoms during the unmixing process in real time. This enables adaptive selection of critical subsets to construct active subspace abundance maps, effectively mitigating spectral redundancy interference. Secondly, we innovatively integrated weighted nuclear norm regularization based on sub-abundance maps into the model, deeply mining potential low-rank structures within spatial distribution patterns to significantly enhance the spatial fidelity of unmixing results. Additionally, a multi-directional neighborhood-aware dual total variation (DTV) regularizer was designed, which enforces spatial consistency constraints between adjacent pixels through a four directional (horizontal, vertical, diagonal, and back-diagonal) differential penalty mechanism, ensuring abundance distributions comply with physical diffusion laws of ground objects. Finally, to efficiently solve the proposed objective model, an optimization algorithm based on the Alternating Direction Method of Multipliers (ADMM) was developed. Comparative experiments conducted on two simulated datasets and four real hyperspectral benchmark datasets, alongside comparisons with state-of-the-art methods, validated the efficiency and superiority of the proposed approach.