This study introduces a unified approach to tackle challenges in both low-level and high-level vision tasks for image processing. The framework integrates faster nonconvex low-rank matrix computations and continuity techniques to yield efficient and high-quality results. In addressing real-world image complexities like noise, variations, and missing data, the framework exploits the intrinsic low-rank structure of the data and incorporates specific residual measurements. The optimization problem for low-rank matrix learning is effectively solved using the nonconvex Proximal Block Coordinate Descent (PBCD) algorithm, resulting in nearly unbiased estimators. Rigorous theoretical analysis ensures both local and global convergence. The PBCD algorithm updates blocks of variables iteratively with closed-form solutions, adeptly handling nonconvexity and promoting faster convergence. Notably, the framework incorporates the randomized singular value decomposition (RSVD) technique and introduces a continuous strategy for adaptive model parameter updates. These strategic choices reduce computational complexity while maintaining result quality. They offer fine-tuned control over the desired rank of the learned matrix and enhance robustness in a straightforward manner. Furthermore, the versatility of the proposed nonconvex PBCD algorithm extends to handling problems with multiple variables, as supported by theoretical analysis. Experimental evaluations, spanning various image low-level and high-level vision tasks such as inpainting, classification, and clustering, validate the effectiveness and efficiency of our framework across diverse databases. The source code is available at .

中文翻译：

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用于图像低级和高级视觉的更快的非凸低秩矩阵学习：统一框架

这项研究引入了一种统一的方法来应对图像处理的低级和高级视觉任务中的挑战。该框架集成了更快的非凸低秩矩阵计算和连续性技术，以产生高效、高质量的结果。在解决现实世界图像的复杂性（例如噪声、变化和丢失数据）时，该框架利用了数据固有的低秩结构并结合了特定的残差测量。使用非凸近端块坐标下降（PBCD）算法有效解决了低秩矩阵学习的优化问题，产生了几乎无偏的估计量。严格的理论分析确保局部和全局的收敛。 PBCD 算法使用封闭式解迭代更新变量块，巧妙地处理非凸性并促进更快的收敛。值得注意的是，该框架结合了随机奇异值分解（RSVD）技术，并引入了自适应模型参数更新的连续策略。这些策略选择降低了计算复杂性，同时保持了结果质量。它们提供对学习矩阵所需等级的微调控制，并以简单的方式增强鲁棒性。此外，正如理论分析所支持的，所提出的非凸 PBCD 算法的多功能性扩展到处理多变量问题。实验评估涵盖各种图像低级和高级视觉任务（例如修复、分类和聚类），验证了我们的框架在不同数据库中的有效性和效率。源代码可在 处获得。