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In this paper, we propose a novel methodology for addressing thehyperspectral image deconvolution problem. This problem is highly ill-posed,and thus, requires proper priors (regularizers) to model the inherentspectral-spatial correlations of the HSI signals. To this end, a newoptimization problem is formulated, leveraging a learnable regularizer in theform of a neural network. To tackle this problem, an effective solver isproposed using the half quadratic splitting methodology. The derived iterativesolver is then expressed as a fixed-point calculation problem within the DeepEquilibrium (DEQ) framework, resulting in an interpretable architecture, withclear explainability to its parameters and convergence properties withpractical benefits. The proposed model is a first attempt to handle theclassical HSI degradation problem with different blurring kernels and noiselevels via a single deep equilibrium model with significant computationalefficiency. Extensive numerical experiments validate the superiority of theproposed methodology over other state-of-the-art methods. This superiorrestoration performance is achieved while requiring 99.85\% less computationtime as compared to existing methods.

An Optimization-based Deep Equilibrium Model for Hyperspectral Image Deconvolution with Convergence Guarantees