基于非局部自相似性和低秩矩阵逼近的补全算法

针对传统矩阵补全算法在图像重建方面的不足，提出了一种基于非局部自相似性和低秩矩阵逼近（NL-LRMA）的补全算法。首先，通过相似性度量找到图像中局部块所对应的非局部相似块，并将相应灰度信息进行向量化，从而构建出非局部相似块矩阵；然后，针对所得相似矩阵的低秩性，对其进行低秩补全操作（LRMA）；最后，对补全结果进行重新组合，以达到恢复原始图像的目的。在灰度图像以及RGB图像上进行重建实验，结果表明：在经典数据集上，NL-LRMA算法要比原LRMA算法在平均峰值信噪比（PSNR）上高出4~7 dB；同时，新算法在视觉效果与PSNR值方面也明显优于迭代重加权核范数（IRNN）、加权核范数（WNNM）、LRMA等传统算法。总之，所提算法对传统算法在自然图像重建方面的不足进行了有效弥补，从而为图像重建提供了一种行之有效的解决方案。

Matrix completion algorithm based on nonlocal self-similarity and low-rank matrix approximation

Aiming at the shortage of traditional matrix completion algorithm in image reconstruction, a completion algorithm based on NonLocal self-similarity and Low Rank Matrix Approximation (NL-LRMA) was proposed. Firstly, the nonlocal similar patches corresponding to the local patches in the image were found through similarity measurement, and the corresponding grayscale matrices were vectorized to construct the nonlocal similar patch matrix. Secondly, aiming at the low-rank property of the obtained similarity matrix, Low-Rank Matrix Approximation (LRMA) was carried out. Finally, the completion results were recombined to achieve the goal of restoring the original image. Reconstruction experiments were performed on grayscale and RGB images. The results show that the average Peak Signal-to-Noise Ratio (PSNR) of NL-LRMA algorithm is 4 dB to 7 dB higher than that of the original LRMA algorithm on a classic dataset; at the same time, NL-LRMA algorithm is better than IRNN (Iteratively Reweighted Nuclear Norm), WNNM (Weighted Nuclear Norm Minimization), LRMA (Low-Rank Matrix Approximation) and other traditional algorithms in the terms of visual effect and PSNR value. In short, NL-LRMA algorithm effectively make up for the shortcomings of traditional algorithms in natural image reconstruction, so as to provide an effective solution for image reconstruction.