# Iterative Singular Tube Hard Thresholding Algorithms for Tensor Recovery

arXiv: https://arxiv.org/abs/2304.04860 · HTML: https://mlsanity.com/paper/2304.04860/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Apr 2023.

## Built on by (most cited first, 1 of 1)

- [Normalized Iterative Hard Thresholding for Tensor Recovery](https://mlsanity.com/paper/2507.04228/) (2025)

## Abstract (arXiv)

Due to the explosive growth of large-scale data sets, tensors have been a vital tool to analyze and process high-dimensional data. Different from the matrix case, tensor decomposition has been defined in various formats, which can be further used to define the best low-rank approximation of a tensor to significantly reduce the dimensionality for signal compression and recovery. In this paper, we consider the low-rank tensor recovery problem when the tubal rank of the underlying tensor is given or estimated a priori. We propose a novel class of iterative singular tube hard thresholding algorithms for tensor recovery based on the low-tubal-rank tensor approximation, including basic, accelerated deterministic and stochastic versions. Convergence guarantees are provided along with the special case when the measurements are linear. Numerical experiments on tensor compressive sensing and color image inpainting are conducted to demonstrate convergence and computational efficiency in practice.