The low-rank recovery is a powerful tool to restore images from incomplete and corrupted observations. Conventional low-rank recovery techniques employ the reweighted nuclear norm minimization, which requires performing the full singular value decomposition and thus is computationally expensive. Using the scheme of bilinear factorization, we propose the Reweighted Low-rank Matrix Factorization (RLMF) method for single channel image restoration. The RLMF method can not only inherit the computational efficiency of bilinear factorization, but also incorporate the empirical distribution of the singular values in natural images. Then, considering the correlation between image channels, we generalize the reweighted nuclear norm from matrices to tensors, and develop the Reweighted Low-rank Tensor Factorization (RLTF) method for multichannel image restoration. Moreover, we enhance the RLMF and RLTF methods by introducing the deep image prior information, which is capable of capturing the implicit image structure through the neural network architecture to improve restoration accuracy. Experimental results show the computational efficiency of the proposed low-rank factorization scheme, and the superior restoration accuracy of the proposed methods compared with the state-of-the-art methods.

中文翻译：

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用于图像恢复的具有深度先验的重新加权低秩分解

低秩恢复是从不完整和损坏的观察中恢复图像的强大工具。传统的低秩恢复技术采用重新加权核范数最小化，这需要执行完整的奇异值分解，因此计算成本很高。使用双线性分解方案，我们提出了用于单通道图像恢复的重加权低秩矩阵分解（RLMF）方法。RLMF方法不仅可以继承双线性分解的计算效率，还可以融合自然图像中奇异值的经验分布。然后，考虑到图像通道之间的相关性，我们将重新加权的核范数从矩阵推广到张量，并开发用于多通道图像恢复的重加权低秩张量分解 (RLTF) 方法。此外，我们通过引入深度图像先验信息来增强 RLMF 和 RLTF 方法，这些信息能够通过神经网络架构捕获隐含的图像结构，以提高恢复精度。实验结果表明了所提出的低秩分解方案的计算效率，以及与最先进的方法相比，所提出的方法具有优越的恢复精度。