In this paper, we propose a multi-matrices low-rank decomposition method for image denoising. In this new method, the total variation (TV) norm is incorporated into low-rank approximation analysis to achieve structural smoothness and to improve quality of the recovered images. Our proposed mathematical framework for multi-matrices low-rank decomposition combines the nuclear norm, TV norm, and $\mathcal {L}_{1}$ norm, which allows us to exploit the low-rank property of natural images, enhance the structural smoothness, and detect and remove large sparse noise. Based on the iterative alternating direction method, we develop an algorithm to solve the proposed challenging optimization problem. We conduct extensive experiments and perform evaluations on multi-images denoising and multi-frames video prediction. Our experimental results demonstrate that the proposed method outperforms the state-of-the-art low-rank matrix recovery methods, particularly for images with large sparse noise.

中文翻译：

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用于图像去噪的具有结构平滑度的多矩阵低秩分解

在本文中，我们提出了一种用于图像去噪的多矩阵低秩分解方法。在这种新方法中，总变异 (TV) 范数被纳入低秩近似分析，以实现结构平滑并提高恢复图像的质量。我们提出的多矩阵低秩分解数学框架结合了核范数、TV 范数和 $\mathcal {L}_{1}$ 范数，这使我们能够利用自然图像的低秩属性，增强结构平滑，检测和去除大的稀疏噪声。基于迭代交替方向方法，我们开发了一种算法来解决所提出的具有挑战性的优化问题。我们对多图像去噪和多帧视频预测进行了广泛的实验和评估。