Orthogonal Constrained Minimization with Tensor $\ell_{2,p}$ Regularization for HSI Denoising and Destriping

📄 arXiv: 2407.03605v3 📥 PDF

作者: Xiaoxia Liu, Shijie Yu, Jian Lu, Xiaojun Chen

分类: math.OC, cs.CV

发布日期: 2024-07-04 (更新: 2025-07-24)

💡 一句话要点

提出多尺度低秩张量正则化方法以解决高光谱图像去噪与去条纹问题

🎯 匹配领域: 支柱五：交互与反应 (Interaction & Reaction)

关键词: 高光谱图像 去噪 去条纹 多尺度低秩 张量正则化 算法收敛 信噪比提升

📋 核心要点

  1. 高光谱图像在实际应用中常受到多种噪声的影响，现有去噪方法难以有效处理复杂噪声。
  2. 本文提出的MLTL2p方法结合了多尺度低秩张量正则化和张量$ ext{l}_{2,p}$范数，通过正交约束最小化来提升去噪效果。
  3. 实验结果显示，MLTL2p方法在模拟和真实HSI数据集上均优于当前最先进的方法，提升了信噪比和视觉质量。

📝 摘要（中文）

高光谱图像（HSIs）常常受到高斯噪声、死线和条纹等多种噪声的污染。本文提出了一种多尺度低秩张量正则化的$ ext{l}{2,p}$（MLTL2p）方法，用于HSI去噪和去条纹。该方法基于新的稀疏增强多尺度低秩张量正则化和张量$ ext{l}{2,p}$范数构建了一个正交约束最小化模型，并提出了具有收敛保证的迭代算法。实验结果表明，MLTL2p方法在均值峰值信噪比等指标上优于现有的深度学习方法，且在视觉质量上表现出色。

🔬 方法详解

问题定义：本文旨在解决高光谱图像去噪和去条纹中的复杂噪声问题。现有方法在处理多种噪声时效果不佳，尤其是在高光谱图像的稀疏性和低秩特性方面存在不足。

核心思路：MLTL2p方法通过引入多尺度低秩张量正则化和张量$ ext{l}_{2,p}$范数，利用全局和局部光谱相关性以及空间非局部自相似性来增强去噪效果。

技术框架：该方法的整体架构包括正交约束最小化模型和一个收敛保证的迭代算法。主要模块包括稀疏增强的高阶奇异值分解和基于张量的正则化。

关键创新：最重要的创新在于提出了稀疏增强的多尺度低秩张量正则化和张量$ ext{l}_{2,p}$范数的扩展，显著提升了低秩性和去条纹效果。

关键设计：在算法设计中，采用了近端块坐标下降算法来解决非凸非光滑的最小化问题，并确保生成序列的任意聚点收敛到一阶平稳点。

📊 实验亮点

实验结果表明，MLTL2p方法在均值峰值信噪比（PSNR）上显著优于现有的深度学习方法，具体提升幅度达到未知，且在视觉质量上也表现出色，验证了该方法的有效性和优越性。

🎯 应用场景

该研究在高光谱图像处理领域具有广泛的应用潜力，尤其是在遥感、医学成像和环境监测等领域。通过有效去除噪声和条纹，能够提高图像的质量和分析的准确性，对相关行业的发展具有重要的实际价值。

📄 摘要（原文）

Hyperspectral images~(HSIs) are often contaminated by a mixture of noise such as Gaussian noise, dead lines, stripes, and so on. In this paper, we propose a multi-scale low-rank tensor regularized $\ell_{2,p}$ (MLTL2p) approach for HSI denoising and destriping, which consists of an orthogonal constrained minimization model and an iterative algorithm with convergence guarantees. The model of the proposed MLTL2p approach is built based on a new sparsity-enhanced Multi-scale Low-rank Tensor regularization and a tensor $\ell_{2,p}$ norm with (p\in (0,1)). The multi-scale low-rank regularization for HSI denoising utilizes the global and local spectral correlation as well as the spatial nonlocal self-similarity priors of HSIs. The corresponding low-rank constraints are formulated based on independent higher-order singular value decomposition with sparsity enhancement on its core tensor to prompt more low-rankness. The tensor $\ell_{2,p}$ norm for HSI destriping is extended from the matrix $\ell_{2,p}$ norm. A proximal block coordinate descent algorithm is proposed in the MLTL2p approach to solve the resulting nonconvex nonsmooth minimization with orthogonal constraints. We show any accumulation point of the sequence generated by the proposed algorithm converges to a first-order stationary point, which is defined using three equalities of substationarity, symmetry, and feasibility for orthogonal constraints. In the numerical experiments, we compare the proposed method with state-of-the-art methods including a deep learning based method, and test the methods on both simulated and real HSI datasets. Our proposed MLTL2p method demonstrates outperformance in terms of metrics such as mean peak signal-to-noise ratio as well as visual quality.