Color Image Recovery Using Generalized Matrix Completion over Higher-Order Finite Dimensional Algebra

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.