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arXiv 2005.04143cs.CV
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全局变分正则化局部非凸低秩矩阵逼近的高光谱图像复原

Hyperspectral Image Restoration via Global Total Variation Regularized Local nonconvex Low-Rank matrix Approximation

Northwest A\&F University, College of Science, Yangling 712100, P.R. China

Haijin Zeng, Xiaozhen Xie, Jifeng Ning

备注：
Accepted for publication in IEEE IGARSS 2020 conference
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摘要：

基于带向全变分（TV）正则化的低秩（LR）模型已被提出用于去除高光谱图像（HSI）中的混合噪声。传统上，LR矩阵的秩使用核范数（NN）近似。NN通过将所有奇异值加在一起来定义，其本质上是奇异值的$L_1$ -范数。它会导致不可忽略的近似误差，因此得到的矩阵估计量可能会有很大的偏差。此外，这些基于频带TV的方法以单独的方式利用空间信息。为了解决这些问题，我们提出了一种空间谱TV（SSTV）正则化非凸局部LR矩阵近似（NonLLRTV）方法来去除混合噪声。从一个方面，使用非凸的$L_γ$范数来公式化HSI的局部LR，这提供了比传统NN更接近矩阵秩的近似。从另一方面，假设HSI在全局空间域中是分段平滑的。TV正则化在保持平滑性和去除高斯噪声方面是有效的。这些事实激发了NonLLR与TV正则化的集成。为了解决带宽TV的局限性，我们使用SSTV正则化同时考虑全局空间结构和相邻波段的谱相关性。实验结果表明，局部非凸惩罚和全局SSTV的使用可以提高空间分段光滑性和整体结构信息的保持。

英文摘要：

Several bandwise total variation (TV) regularized low-rank (LR)-based models have been proposed to remove mixed noise in hyperspectral images (HSIs). Conventionally, the rank of LR matrix is approximated using nuclear norm (NN). The NN is defined by adding all singular values together, which is essentially a $L_1$-norm of the singular values. It results in non-negligible approximation errors and thus the resulting matrix estimator can be significantly biased. Moreover, these bandwise TV-based methods exploit the spatial information in a separate manner. To cope with these problems, we propose a spatial-spectral TV (SSTV) regularized non-convex local LR matrix approximation (NonLLRTV) method to remove mixed noise in HSIs. From one aspect, local LR of HSIs is formulated using a non-convex $L_γ$-norm, which provides a closer approximation to the matrix rank than the traditional NN. From another aspect, HSIs are assumed to be piecewisely smooth in the global spatial domain. The TV regularization is effective in preserving the smoothness and removing Gaussian noise. These facts inspire the integration of the NonLLR with TV regularization. To address the limitations of bandwise TV, we use the SSTV regularization to simultaneously consider global spatial structure and spectral correlation of neighboring bands. Experiment results indicate that the use of local non-convex penalty and global SSTV can boost the preserving of spatial piecewise smoothness and overall structural information.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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