Hyperspectral images (HSIs) are often degraded by a mixture of various types of noise during the imaging process, including Gaussian noise, impulse noise, and stripes. Such complex noise could plague the subsequent HSIs processing. Generally, most HSI denoising methods formulate sparsity optimization problems with convex norm constraints, which over-penalize large entries of vectors, and may result in a biased solution. In this paper, a nonconvex regularized low-rank and sparse matrix decomposition (NonRLRS) method is proposed for HSI denoising, which can simultaneously remove the Gaussian noise, impulse noise, dead lines, and stripes. The NonRLRS aims to decompose the degraded HSI, expressed in a matrix form, into low-rank and sparse components with a robust formulation. To enhance the sparsity in both the intrinsic low-rank structure and the sparse corruptions, a novel nonconvex regularizer named as normalized ε -penalty, is presented, which can adaptively shrink each entry. In addition, an effective algorithm based on the majorization minimization (MM) is developed to solve the resulting nonconvex optimization problem. Specifically, the MM algorithm first substitutes the nonconvex objective function with the surrogate upper-bound in each iteration, and then minimizes the constructed surrogate function, which enables the nonconvex problem to be solved in the framework of reweighted technique. Experimental results on both simulated and real data demonstrate the effectiveness of the proposed method.

中文翻译：

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通过非凸正则化低秩和稀疏矩阵分解对高光谱图像进行降噪。

高光谱图像（HSI）通常在成像过程中由于各种类型的噪声（包括高斯噪声，脉冲噪声和条纹）的混合而退化。这种复杂的噪声可能会困扰随后的HSI处理。通常，大多数HSI降噪方法会制定具有凸范数约束的稀疏性优化问题，这会过度惩罚矢量的大项，并可能导致有偏差的解决方案。本文提出了一种非凸正则化低秩和稀疏矩阵分解（NonRLRS）方法进行HSI去噪，该方法可以同时去除高斯噪声，脉冲噪声，死线和条纹。NonRLRS旨在通过强大的公式将以矩阵形式表示的降解后的HSI分解为低秩和稀疏成分。为了提高固有低秩结构和稀疏损坏的稀疏性，提出了一种新颖的非凸正则化器，称为归一化ε-罚分，它可以自适应地缩小每个条目。此外，开发了一种基于主化最小化（MM）的有效算法来解决由此产生的非凸优化问题。具体地说，MM算法首先在每次迭代中用代理上限代替非凸目标函数，然后最小化构造的代理函数，这使得非凸问题能够在加权技术的框架内得以解决。模拟和真实数据的实验结果证明了该方法的有效性。可以自适应地缩小每个条目。此外，开发了一种基于主化最小化（MM）的有效算法来解决由此产生的非凸优化问题。具体地说，MM算法首先在每次迭代中用代理上限代替非凸目标函数，然后最小化构造的代理函数，这使得非凸问题能够在加权技术的框架内得以解决。模拟和真实数据的实验结果证明了该方法的有效性。可以自适应地缩小每个条目。此外，开发了一种基于主化最小化（MM）的有效算法来解决由此产生的非凸优化问题。具体地说，MM算法首先在每次迭代中用代理上限代替非凸目标函数，然后最小化构造的代理函数，这使得非凸问题能够在加权技术的框架内得以解决。模拟和真实数据的实验结果证明了该方法的有效性。MM算法首先在每次迭代中用代理上限代替非凸目标函数，然后最小化构造的代理函数，这使得非凸问题可以在加权技术的框架内解决。模拟和真实数据的实验结果证明了该方法的有效性。MM算法首先在每次迭代中用代理上限代替非凸目标函数，然后最小化构造的代理函数，这使得非凸问题可以在加权技术的框架内解决。模拟和真实数据的实验结果证明了该方法的有效性。