Abstract
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 multiway delay embedding transform of the recovered higherorder tensor. Our experiments showed that the proposed
method successfully recovered missing slices for some color
images and functional magnetic resonance images