Conventional low-rank (LR)-based hyperspectral image (HSI) denoising models generally convert high-dimensional data into 2-D matrices or just treat this type of data as 3-D tensors. However, these pure LR or tensor low-rank (TLR)-based methods lack flexibility for considering different correlation information from different HSI directions, which leads to the loss of comprehensive structure information and inherent spatial–spectral relationship. To overcome these shortcomings, we propose a novel multidirectional LR modeling and spatial–spectral total variation (MLR-SSTV) model for removing HSI mixed noise. By incorporating the weighted nuclear norm, we obtain the weighted sum of weighted nuclear norm minimization (WSWNNM) and the weighted sum of weighted tensor nuclear norm minimization (WSWTNNM) to estimate the more accurate LR tensor, especially, to remove the dead-line noise better. Gaussian noise is further denoised and the local spatial–spectral smoothness is preserved effectively by SSTV regularization. We develop an efficient algorithm for solving the derived optimization based on the alternating direction method of multipliers (ADMM). Extensive experiments on both synthetic data and real data demonstrate the superior performance of the proposed MLR-SSTV model for HSI mixed noise removal.

中文翻译：

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基于多方向低秩建模和空间光谱总变化的高光谱图像混合噪声去除

常规的基于低秩（LR）的高光谱图像（HSI）去噪模型通常将高维数据转换为2D矩阵，或者仅将此类数据视为3D张量。但是，这些基于纯LR或张量低秩（TLR）的方法缺乏考虑来自不同HSI方向的不同相关信息的灵活性，这导致综合结构信息和固有的空间光谱关系丢失。为了克服这些缺点，我们提出了一种新颖的多方向LR建模和空间光谱总变化（MLR-SSTV）模型，用于消除HSI混合噪声。通过合并加权核规范，我们获得加权核规范最小化（WSWNNM）的加权总和和加权张量核规范最小化（WSWTNNM）的加权总和，以估计更准确的LR张量，特别是，更好地消除死线噪声。通过SSTV正则化，可以进一步对高斯噪声进行降噪，并有效保留局部空间光谱的平滑度。我们开发了一种基于乘法器交替方向法（ADMM）的求解派生优化的有效算法。在合成数据和真实数据上的大量实验证明了所提出的MLR-SSTV模型在HSI混合噪声去除方面的优越性能。