In this paper, we propose a novel nonconvex approach to robust principal component analysis for HSI denoising, which focuses on simultaneously developing more accurate approximations to both rank and column-wise sparsity for the low-rank and sparse components, respectively. In particular, the new method adopts the log-determinant rank approximation and a novel $\ell_{2,\log}$ norm, to restrict the local low-rank or column-wisely sparse properties for the component matrices, respectively. For the $\ell_{2,\log}$-regularized shrinkage problem, we develop an efficient, closed-form solution, which is named $\ell_{2,\log}$-shrinkage operator. The new regularization and the corresponding operator can be generally used in other problems that require column-wise sparsity. Moreover, we impose the spatial-spectral total variation regularization in the log-based nonconvex RPCA model, which enhances the global piece-wise smoothness and spectral consistency from the spatial and spectral views in the recovered HSI. Extensive experiments on both simulated and real HSIs demonstrate the effectiveness of the proposed method in denoising HSIs.

翻译：在本文中,我们提出一种新型的非混凝土方法,用于对氢氟碳化物分解工作进行稳健的主要组成部分分析,该方法侧重于分别为低级和稀散的部件分别制定更精确的军阶和军列宽度近似值,特别是,新方法采用了对数-定级近似值和新颖的美元=2,\log}标准,以限制部件矩阵的低级或分栏稀释性特性。对于美元(ell)2,\log}美元(正规化)的萎缩问题,我们开发了一个高效的封闭式解决方案,称为$\ell ⁇ 2,\log}美元(缩水)-平面操作器。新的正规化和相应的操作器通常用于需要分栏宽度的其他问题。此外,我们将空间光谱总变异常调适用于基于日志的非convex RPCA 模型,该模型从回收的HSI的空间和光谱观点中提高全球的片度平滑度和光谱一致性。关于模拟和真实的HSI的大规模实验,展示了模拟和真实的HSI脱色方法的有效性。