NSR-Net: Representation Model-Inspired Interpretable Deep Unfolding Network for Hyperspectral Image Classification

Deep learning-based methods have demonstrated promising performance in hyperspectral image (HSI) classification. However, the black-box nature of deep learning poses a significant challenge in designing effective network architectures for HSI classification. To overcome this issue, this article presents a representation model-inspired interpretable deep unfolding network (NSR-Net). First, we formulate a deep-constrained nonnegative sparse representation (NSR) model with enhanced generalization ability to address the limitations of the prior-constrained NSR, i.e., its reliance on manual priors and specific assumptions. Second, the solving process for deep-constrained NSR is unfolded into a deep network, with each component of the network corresponding directly to a specific step. Finally, following the principle of representation model-based classification, a subdictionary reconstruction module (SDRM) is designed to determine the class label. In SDRM, each subdictionary is learned through a context-integrated training process, resulting in superior discriminative capability. In addition, to better guide NSR-Net optimization, we introduce a new composite loss function, which consists of constraint loss and residual loss, aiming to effectively recover representation coefficients and reconstruct data from the subdictionary. Experiments conducted on four distinct HSI datasets illustrate the superiority and generalization performance of the proposed method compared with advanced representation model-based and deep learning-based methods, with overall accuracy (OA) improvements of 0.72%–9.80%, 1.39%–8.09%, 0.40%–5.85%, and 0.56%–6.84% for Indian Pines, Salinas, LongKou, and Loukia, respectively. The source code will be available at: <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/ZhaohuiXue/NSR-Net</uri>.