论文标题
高光谱图像恢复通过全球总变异正规局部非凸低矩阵近似
Hyperspectral Image Restoration via Global Total Variation Regularized Local nonconvex Low-Rank matrix Approximation
论文作者
论文摘要
已经提出了几种带状的总变异（TV）正规化低级别（LR）模型，以消除高光谱图像（HSIS）中的混合噪声。通常，使用核标准（NN）近似LR矩阵的等级。 NN的定义是通过将所有单数值添加在一起，这本质上是单数值的$ L_1 $ norm。它导致不可忽略的近似误差，因此所得的矩阵估计器可能会显着偏差。此外，这些基于带电视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）正则非凸局LR矩阵近似（NONLLRTV）方法，以消除HSIS中的混合噪声。从一个方面，使用非convex $l_γ$ -NORM制定了HSIS的本地LR，该非凸$L_γ$ -Norm比传统NN提供了更接近矩阵等级的近似值。从另一方面，假定HSI在整体空间域中是单独平滑的。电视正规化可有效地保留光滑度和消除高斯噪声。这些事实激发了非LLL与电视正则化的整合。为了解决带电视的局限性，我们使用SSTV正则化来同时考虑相邻频段的全局空间结构和光谱相关性。实验结果表明，使用局部非凸惩罚和全球SSTV可以提高空间分段平滑度和整体结构信息。
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.
