A Highly Interpretable Deep Equilibrium Network for Hyperspectral Image Deconvolution

Abstract

In this paper, a novel technique for the hyperspectral image deconvolution problem is developed. First, considering the highly ill-posed nature of the examined problem, it is imperative to incorporate proper priors (regularizers) to capture the strong spectral and spatial dependencies of the hyperspectral images. Then, in light of this, a novel optimization problem is proposed by employing a convolutional neural network to act as a regularizer, which is learnt to reflect the properties of the signals of interest. To solve the proposed optimization problem, we use the half quadratic splitting methodology, thus designing an efficient iterative solver (iteration map). Based on the Deep Equilibrium (DEQ) modeling, which aims to express the proposed iterative solver as an equilibrium (fixed-point) computation, a highly interpretable deep learning-based network is derived, which can be trained endto-end. Extensive numerical results using two publicly available datasets illustrate that the proposed method markedly outperforms other state-of-the-art approaches.