Ali Shojaeifard - Department of Mathematics and Statistics, ‎Faculty and Institute of Basic Sciences, ‎Imam Hossein Comprehensive University‎, ‎Tehran‎, ‎Iran
Hamid Reza Yazdani - Department of Mathematics and Statistics, ‎Faculty and Institute of Basic Sciences, ‎Imam Hossein Comprehensive University‎, ‎Tehran‎, ‎Iran
Mohsen Shahrezaee - Department of Defense and Engineering, ‎Imam Hossein Comprehensive University‎, ‎Tehran‎, ‎Iran

In this paper‎, ‎we are going to analyze big data (embedded in the digital images) with new methods of tensor completion (TC)‎. ‎The determination of tensor ranks and the type of decomposition are significant and essential matters‎. ‎For defeating these problems‎, ‎Bayesian CP-Factorization (BCPF) is applied to the tensor completion problem‎. ‎The \textit{BCPF} can optimize the type of ranks and decomposition for achieving the best results‎. ‎In this paper‎, ‎the hybrid method is proposed by integrating BCPF and general TC‎. ‎The tensor completion problem was briefly introduced‎. ‎Then‎, ‎based on our implementations‎, ‎and related sources‎, ‎the proposed tensor-based completion methods emphasize their strengths and weaknesses‎. ‎Theoretical‎, ‎practical‎, ‎and applied theories have been discussed and two of them for analyzing big data have been selected‎, ‎and applied to several examples of selected images‎. ‎The results are extracted and compared to determine the method's efficiency and importance compared to each other‎. ‎Finally‎, ‎the future ways and the field of future activity are also presented.

Image Recovery‎, ‎Matrix Completion‎, ‎Optimization Problems‎, ‎Tensor Completion‎, ‎Variational Bayesian inference