Weighted Strong Product Graph Laplacian Regularization for Hyperspectral Image Mixed-Noise Removal with Superpixel Segmentation

Hyperspectral images (HSIs) are inevitably degraded by mixed noise, which hampers downstream interpretation. Recent graph-signal-processing denoisers encode the spatial–spectral structure of an HSI through a product graph over superpixel bodies, yet the adopted Kronecker (tensor) product graph retains only the joint spatial–spectral edges and discards the pure-spatial and pure-spectral edges—the two priors that govern HSI smoothness. We introduce a two-parameter weighted product-graph family that contains the Kronecker, Cartesian and strong products as exact special cases, and propose Weighted Strong Product Graph Laplacian Regularization (WSPGLR)—the strong-product branch with a tunable joint-edge weight β—embedded in a global low-rank plus sparse model solved by the Alternating Direction Method of Multipliers (ADMM) with singular-value-thresholding and soft-thresholding updates and a sparse conjugate-gradient (CG) solve. On three simulated cubes (Washington DC Mall, Pavia University, Indian Pines) under four mixed-noise scenarios, WSPGLR consistently improves Mean Peak Signal-to-Noise Ratio (MPSNR) and ERGAS (Erreur Relative Globale Adimensionnelle de Synthèse) over a matched Kronecker-product control in every tested case (and Mean Structural Similarity (MSSIM) in 11 of 12 settings)—up to 2.5 dB in MPSNR from the graph term alone—and an ablation shows that β governs a spatial–spectral fidelity trade-off (Spectral Angle Mapper, SAM). On the detailed urban scenes, WSPGLR attains the highest MPSNR against the external methods and matched control in seven of eight settings, whereas it trails LRTDTV on the smooth agricultural scene; with an optional scene-adaptive TV step it attains the best average rank across scene types; a Tucker-based variant further shows the low-rank block is modular and generally improves spectral fidelity. Tests on four no-reference real HSIs and 30 paired real-noise MEHSI samples extend the sensor coverage; on MEHSI, the native-domain RND framework remains substantially stronger, which delimits the scope of the proposed training-free regularizer.