# Regularized Kaczmarz Algorithms for Tensor Recovery

arXiv: https://arxiv.org/abs/2102.06852 · HTML: https://mlsanity.com/paper/2102.06852/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Feb 2021.

## Built on by (most cited first, 2 of 2)

- [Power of ℓ1-Norm Regularized Kaczmarz Algorithms for High-Order Tensor Recovery](https://mlsanity.com/paper/2405.08275/) (2024)
- [Quantile-Based Randomized Kaczmarz for Corrupted Tensor Linear Systems](https://mlsanity.com/paper/2503.18190/) (2025)

## Abstract (arXiv)

Tensor recovery has recently arisen in a lot of application fields, such as transportation, medical imaging and remote sensing. Under the assumption that signals possess sparse and/or low-rank structures, many tensor recovery methods have been developed to apply various regularization techniques together with the operator-splitting type of algorithms. Due to the unprecedented growth of data, it becomes increasingly desirable to use streamlined algorithms to achieve real-time computation, such as stochastic optimization algorithms that have recently emerged as an efficient family of methods in machine learning. In this work, we propose a novel algorithmic framework based on the Kaczmarz algorithm for tensor recovery. We provide thorough convergence analysis and its applications from the vector case to the tensor one. Numerical results on a variety of tensor recovery applications, including sparse signal recovery, low-rank tensor recovery, image inpainting and deconvolution, illustrate the enormous potential of the proposed methods.