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 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.