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Consistent MDT-Tucker: A Hankel Structure Constrained Tucker Decomposition in Delay Embedded Space

When Multiway Delay-embedding Transform (MDT) is applied on the signal such as an image or a video, it is transformed into a high-dimensional tensor with Hankel and low-rank structures. Tensor completion methods using MDT perform completion with respect to this higher-order tensor. However, the completed tensor loses the Hankel structure by obtaining its low-rank approximation in many methods using MDT. In our study, we focus on MDT-Tucker [1], a method of low-rank tensor completion, and propose Consistent MDT-Tucker, a method of completion that preserves the Hankel structure. We show its monotonic convergence property based on majorization-minimization method. We also show that Consistent MDT-Tucker gives another interpretation of Fast MDT-Tucker [2], the very fast and efficient method for solving MDT-Tucker. In our experiments, we compare the image recovery performances between MDT-Tucker and Consistent MDT-Tucker and confirm that the completion performance remains almost the same, with a slight improvement in convergence speed.