Hyperspectral image denoising via cooperated self-supervised CNN transform and nonconvex regularization

Methods that leverage the sparsity and the low-rankness in the transformed domain have gained growing interest for hyperspectral image (HSI) denoising. Recently, many researches simultaneously utilizing low-rankness and local smoothness have emerged. Although these approaches achieve great denoising performance, they exhibit several limitations. First, the widely adopted $l_1$ norm is a biased function, potentially leading to blurring edges. Second, employing tensor singular value decomposition (T-SVD) to ensure low-rankness brings a heavy computational burden. Additionally, the manually designed regularization norm is fixed for all testing data, which may cause a generalization problem. To address these challenges, this work proposes a novel optimization model for HSI denoising that incorporates the self-supervised CNN transform and TV regularization (CTTV) with the nonconvex function induced norm. The CNN-based transform could implicitly ensure the low-rankness of the tensor and learn the potential information in the noisy data. Furthermore, we exploit the unbiased nonconvex minimax concave penalty (MCP) to enforce the local smoothness of the extracted features while preserving sharp edges. We design an algorithm to solve the proposed model built on the hybrid of the half-quadratic splitting (HQS) and the alternating direction method of multipliers (ADMM), in which the network parameter and the denoised image are separately optimized. Extensive experiments on various datasets indicate that our proposed method can achieve state-of-the-art performance in HSI denoising.