Iterative tensor eigen rank minimization for low-rank tensor completion

By minimizing the tensor ranks, recent methods exploit the tensor spatial correlation between the tensor entries for the low-rank tensor completion (TC) problem. However, these methods suffer from the difficulty in sufficiently exploiting the tensor spatial correlation, which reduces the TC performance. To tackle such difficulty, this paper defines a novel tensor rank called the tensor eigen rank for the low-rank TC problem. Specifically, the novel tensor rank is obtained from a tensor transformation, which directly transforms an arbitrary-order tensor into a tensor pile. By minimizing the novel tensor rank, we subsequently establish a low-rank TC model. Within the framework of the iterative shrinkage and thresholding scheme, an algorithm named iterative tensor eigen rank minimization (IterMin) is further proposed to address the established model. To verify the effectiveness of the proposed method, we investigate the TC observing probability, model recovery error, algorithm convergence, and algorithm complexity. The experiments on the synthetic and real-world datasets show that the proposed method outperforms several state-of-the-art methods in terms of the quantitative and visual results.