Superpixel guided weighted low-rank representation for nonlinear hyperspectral unmixing

The Generalized Bilinear Mixing model (GBM) has gained significant prominence in the field of nonlinear hyperspectral image unmixing, with recent advancements utilizing superpixel segmentation for the extraction of homogeneous patches. However, the application of the Low-Rank Representation (LRR) constraint to each superpixel has been observed to disproportionately diminish smaller singular values, resulting in associated challenges. Building upon our prior investigation of the weighted LRR (WLRR) approach within the robust GBM model, which effectively mitigated bias by assigning appropriate weights to singular values, we extend this framework in the current study. Here, we employ entropy rate superpixel (ERS) segmentation to extract homogeneous patches, applying the weighted low-rank constraint and developing the robust GBM model (RGM-SG-WLRR) for nonlinear unmixing analysis. The proposed model is effectively solved using the Alternating Direction Method of Multipliers (ADMM) iterative scheme. Through extensive experimental analyses conducted on both simulated and real data cubes, our findings highlight the superior performance of the RGM-SG-WLRR model over alternative methods, as evidenced by its notable improvements in terms of root-mean-square error and signal-to-reconstruction error.