To improve the accuracy of color image completion with missing entries, we present a recovery method based on generalized higher-order scalars. We extend the traditional second-order matrix model to a more comprehensive higher-order matrix equivalent, called the "t-matrix" model, which incorporates a pixel neighborhood expansion strategy to characterize the local pixel constraints. This "t-matrix" model is then used to extend some commonly used matrix and tensor completion algorithms to their higher-order versions. We perform extensive experiments on various algorithms using simulated data and algorithms on simulated data and publicly available images and compare their performance. The results show that our generalized matrix completion model and the corresponding algorithm compare favorably with their lower-order tensor and conventional matrix counterparts.

基于广义高阶标量的恢复方法，扩展传统的二阶矩阵模型到更全面的高阶矩阵模型，称为“t-矩阵”模型，采用像素邻域扩展策略来描述局部像素约束。我们在模拟数据和公开可用的图像上对各种算法进行了大量实验，并比较了它们的性能。结果表明，我们的广义矩阵补全模型及相应算法与低阶张量和传统矩阵对应物相比具有显著优势。

基于广义矩阵补全的高阶有限维代数色彩图像恢复