Hyperspectral Image Restoration Guided by Joint Statistical Characterization of Noise

Images obtained from hyperspectral sensors provide visual details about the target area beyond the visible parts of the electromagnetic spectrum. However, the acquired 3-D datacube is corrupted by a combination of mixed Gaussian-impulse noise. In this letter, the problem is posed as the joint statistical characterization of this mixed noise scenario which is missing in the recent literature. We propose a dual-fidelity-based ( $\ell _{2}$ - and $\ell _{1}$ -norms) automated parameter adjustment (Dual-FAPA) scheme for recovering hyperspectral images (HSIs) corrupted by the mixed noise. Total variation (TV) is used as the regularization term due to its noise removal and detail-preserving capability. To estimate the bounds on the aggregate expected absolute value (EAV) and variance under joint Gaussian and impulse noise, the objective function is remodeled as a constrained minimization problem whose solution aids in the automated selection of the parameters $(\alpha _{1},~\alpha _{2})$ used to handle different levels of noise. Furthermore, the mathematical tractability of the solution based on iterative monotonic solution and convergence analysis suggest the robustness of the proposed methodology. On experimentation with synthetic and real HSI data, we observe a significant improvement over state-of-the-art methods by multiple qualitative and quantitative assessments.