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

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.

Simultaneously Low Rank and Group Sparse Decomposition for Rolling Bearing Fault Diagnosis

“…Also, this process is regards as a standard DET. For a rigorous expression of the DET, we define as the duplication matrix, which satisfies [ 45 ]: …”

Manifold Modeling in Embedded Space: An Interpretable Alternative to Deep Image Prior

“…A related technique, low-rank tensor modeling in embedded space, was recently studied by [75]. However, the modeling approaches here are quite different since it considered the multilinear approach, while we consider the nonlinear (manifold) approach.…”

“…However, the modeling approaches here are quite different since it considered the multilinear approach, while we consider the nonlinear (manifold) approach. Thus, our study can be interpreted as a manifold version of [75] from the perspective of tensor completion methods. Note that Yokota et al [75] applied their model to only the tensor completion task.…”

“…Thus, our study can be interpreted as a manifold version of [75] from the perspective of tensor completion methods. Note that Yokota et al [75] applied their model to only the tensor completion task. Moreover, in this study, we investigated not only the tensor completion but also superresolution, deconvolution, and denoising tasks.…”

Tensor Completion Based on Triple Tubal Nuclear Norm

“…To decrease the sample complexity of TriTNN, it will be helpful to follow the suggestions in [44] to design new atomic norms like [46]. To get better visual completion performances, the authors would like to consider adding smoothness regularization in the model like [47][48][49] and adopting different tensorization methods like [50]. It is also helpful for studying new tensor completion models using deep neural networks [51].…”