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Let us consider a case where all of the elements in some continuous slicesare missing in tensor data.  In this case, the nuclear-norm and total variation regularization methodsusually fail to recover the missing elements.  The key problem is capturing some delay/shift-invariant structure.  In this study, we consider a low-rank model in an embedded space of a tensor.  For this purpose, we extend a delay embedding for a time series to a"multi-way delay-embedding transform" for a tensor, which takes a givenincomplete tensor as the input and outputs a higher-order incomplete Hankeltensor.  The higher-order tensor is then recovered by Tucker-based low-rank tensorfactorization.  Finally, an estimated tensor can be obtained by using the inverse multi-waydelay embedding transform of the recovered higher-order tensor.  Our experiments showed that the proposed method successfully recoveredmissing slices for some color images and functional magnetic resonance images.

Missing Slice Recovery for Tensors Using a Low-rank Model in Embedded Space