Weighted Residual NMF for Hyperspectral Image Unmixing Based on an Adaptive Spatial-Spectral Constraint

‍ ‍When the standard nonnegative matrix factorization （NMF） model was applied to hyperspectral image unmixing，the nonconvexity of the model and insufficient utilization of spectral and spatial prior information resulted in low unmixing accuracy. To improve the unmixing performance， a weighted residual NMF for hyperspectral image unmixing based on an adaptive spatial-spectral constraint was proposed. The algorithm initially enhanced the traditional NMF model by utilizing the residuals between the original hyperspectral and reconstructed image matrices in the iterative process to construct the residual weight factors. This algorithm assigned contribution weights to each row of the loss function to alleviate the influence of noise and improve its robustness. Additionally， to leverage the rich a priori information in hyperspectral images， the algorithm introduced pixel spatial-spectral similarity to gauge the similarity between pixels， capturing the spatial and spectral connections among them. It then constructed the spatial weight factors by adaptively determining the pixel neighborhoods from the similarity matrix， thereby enhancing the piecewise smoothing of the abundance. Moreover， spectral weighting factors were constructed by integrating the inherent characteristics of the abundance matrix， which promoted the sparsity of the abundance. Finally， owing to the high spectral resolution of hyperspectral images and small variation in reflection values between adjacent bands， the endmember spectra exhibit a certain degree of smoothness. The algorithm assigned smoothing weights using the differences between the spectral reflectance values of endmembers to adjust the degree of spectral smoothing of the endmembers during the iterative process. This study utilized gradient descent to derive the multiplicative update rules for the algorithm. To demonstrate the effectiveness of the proposed algorithm， it was compared with several other algorithms using simulated data as well as two real hyperspectral datasets， namely， Jasper Ridge and Urban. The experimental results validate that the proposed algorithm exhibits superior unmixing performance.