# Power of ℓ1-Norm Regularized Kaczmarz Algorithms for High-Order Tensor Recovery

arXiv: https://arxiv.org/abs/2405.08275 · HTML: https://mlsanity.com/paper/2405.08275/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 36 references that are in the map.
- First posted on arXiv 14 May 2024.

## Builds on (most cited first, 9 of 9)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [Guaranteed Tensor Recovery Fused Low-rankness and Smoothness](https://mlsanity.com/paper/2302.02155/) (2023)
- [Faster randomized block Kaczmarz algorithms](https://mlsanity.com/paper/1902.09946/) (2019)
- [Tensor-Tensor Product Toolbox](https://mlsanity.com/paper/1806.07247/) (2018)
- [The Linearized Bregman Method via Split Feasibility Problems: Analysis and Generalizations](https://mlsanity.com/paper/1309.2094/) (2013)
- [The Proximity Operator of the Log-Sum Penalty](https://mlsanity.com/paper/2103.02681/) (2021)
- [Regularized Kaczmarz Algorithms for Tensor Recovery](https://mlsanity.com/paper/2102.06852/) (2021)
- [Log-Sum Regularized Kaczmarz Algorithms for High-Order Tensor Recovery](https://mlsanity.com/paper/2311.00783/) (2023)

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

- [Separable Nonnegative Matrix Factorization Using Powered Ratio-of-Norms Regularization](https://mlsanity.com/paper/2608.28799/) (2026)

## Abstract (arXiv)

Tensors serve as a crucial tool in the representation and analysis of complex, multi-dimensional data. As data volumes continue to expand, there is an increasing demand for developing optimization algorithms that can directly operate on tensors to deliver fast and effective computations. Many problems in real-world applications can be formulated as the task of recovering high-order tensors characterized by sparse and/or low-rank structures. In this work, we propose novel Kaczmarz algorithms with a power of the ℓ1-norm regularization for reconstructing high-order tensors by exploiting sparsity and/or low-rankness of tensor data. In addition, we develop both a block and an accelerated variant, along with a thorough convergence analysis of these algorithms. A variety of numerical experiments on both synthetic and real-world datasets demonstrate the effectiveness and significant potential of the proposed methods in image and video processing tasks, such as image sequence destriping and video deconvolution.