Color Image Recovery Using Generalized Matrix Completion over
  Higher-Order Finite Dimensional Algebra
Liang Liao Zhuang Guo Qi Gao Yan Wang Fajun Yu Qifeng Zhao Stephen Johh Maybank
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.