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

• URL: http://arxiv.org/abs/2306.06378v1
• Date: Sat, 10 Jun 2023 08:25:16 GMT
• Title: An Optimization-based Deep Equilibrium Model for Hyperspectral Image Deconvolution with Convergence Guarantees
• Authors: Alexandros Gkillas, Dimitris Ampeliotis, Kostas Berberidis
• Abstract summary: We propose a novel methodology for addressing the hyperspectral image deconvolution problem. A new optimization problem is formulated, leveraging a learnable regularizer in the form of a neural network. The derived iterative solver is then expressed as a fixed-point calculation problem within the Deep Equilibrium framework.
• Score: 71.57324258813675
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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