Missing Slice Recovery for Tensors Using a Low-rank Model in Embedded Space.
2018
Let us consider a case where all of the elements in some continuous slices are missing in tensor data.
In this case, the nuclear-norm and total variation regularization methods usually 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 given incomplete tensor as the input and outputs a higher-order incomplete Hankel tensor.
The higher-order tensor is then recovered by Tucker-based low-rank tensor factorization.
Finally, an estimated tensor can be obtained by using the inverse multi-way delay embedding transform of the recovered higher-order tensor.
Our experiments showed that the proposed method successfully recovered missing slices for some color images and functional magnetic resonance images.
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