An Optimization-based Deep Equilibrium Model for Hyperspectral Image
  Deconvolution with Convergence Guarantees
Alexandros Gkillas Dimitris Ampeliotis Kostas Berberidis
In this paper, we propose a novel methodology for addressing the
hyperspectral image deconvolution problem. This problem is highly ill-posed,
and thus, requires proper priors (regularizers) to model the inherent
spectral-spatial correlations of the HSI signals. To this end, a new
optimization problem is formulated, leveraging a learnable regularizer in the
form of a neural network. To tackle this problem, an effective solver is
proposed using the half quadratic splitting methodology. The derived iterative
solver is then expressed as a fixed-point calculation problem within the Deep
Equilibrium (DEQ) framework, resulting in an interpretable architecture, with
clear explainability to its parameters and convergence properties with
practical benefits. The proposed model is a first attempt to handle the
classical HSI degradation problem with different blurring kernels and noise
levels via a single deep equilibrium model with significant computational
efficiency. Extensive numerical experiments validate the superiority of the
proposed methodology over other state-of-the-art methods. This superior
restoration performance is achieved while requiring 99.85\% less computation
time as compared to existing methods.