IEEE Trans Image Process. 2020;29:44-56. doi: 10.1109/TIP.2019.2926736. Epub 2019 Jul 12.
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.
高光谱图像（HSI）在成像过程中经常受到多种类型噪声的混合影响，包括高斯噪声、脉冲噪声和条纹。这种复杂的噪声会影响后续的 HSI 处理。一般来说，大多数 HSI 去噪方法都采用具有凸范数约束的稀疏优化问题，这会过度惩罚向量的大元素，可能导致有偏差的解。本文提出了一种用于 HSI 去噪的非凸正则化低秩和稀疏矩阵分解（NonRLRS）方法，它可以同时去除高斯噪声、脉冲噪声、死线和条纹。NonRLRS 的目的是将以矩阵形式表示的退化 HSI 分解为具有鲁棒公式的低秩和稀疏分量。为了增强固有低秩结构和稀疏伪影的稀疏性，提出了一种新的非凸正则化项，即归一化 ε-惩罚项，可以自适应地收缩每个元素。此外，还开发了一种基于乘子最小化（MM）的有效算法来解决由此产生的非凸优化问题。具体来说，MM 算法首先在每次迭代中用替代上界替代非凸目标函数，然后最小化构造的替代函数，这使得非凸问题可以在加权技术的框架内得到解决。在模拟和真实数据上的实验结果表明了该方法的有效性。
