Joint Hyperspectral Image Deconvolution and Unmixing via Plug-and-Play Priors

Hyperspectral imaging (HSI) provides rich spatial and spectral information for remote sensing, mineral exploration, and biomedical analysis, but its limited spatial resolution and sensor imperfections lead to blurred, noisy, and mixed-pixel observations. Addressing these degradations jointly—rather than sequentially—has been shown to improve physical interpretability, yet existing joint deblurring–unmixing methods rely primarily on hand-crafted regularizers that do not fully exploit spatial–spectral structure. Meanwhile, recent plug-and-play (PnP) approaches applied to HSI leverage deep priors but focus solely on either deconvolution or unmixing in isolation. To bridge this gap, we formulate the joint inverse problem of hyperspectral deblurring and spectral unmixing and propose, to our knowledge, the first plug-and-play framework tailored for this coupled task using the Alternating Direction Method of Multipliers (ADMM) and a pretrained deep denoiser (DnCNN) as an implicit PnP prior. Our method uses the natural splitting properties of ADMM to separate a physics-driven subproblem that enforces fidelity to the hyperspectral forward model, which includes linear mixing and blur under a linear, space-invariant convolution approximation, from the data-driven prior step. This synergy of model-based fidelity and learned spatial prior enables more accurate abundance estimates than those obtained with approaches relying solely on analytical regularizers. Experimental results on real hyperspectral datasets demonstrate that the proposed Plug-and-Play Joint Deconvolution and Unmixing (PnP-JDU) method outperforms conventional unmixing baselines, stand-alone PnP unmixing methods, and the Deblurring and Sparse Unmixing via the Alternating Direction Method with Total Variation (DSUnADM-TV) baseline in reconstruction and abundance accuracy metrics. Across the tested datasets and imaging conditions, PnP-JDU achieves lower RMSE, higher PSNR, lower reconstruction and abundance errors, and lower SAD values, while preserving fine spatial details and producing physically meaningful abundance maps.