# Log-Sum Regularized Kaczmarz Algorithms for High-Order Tensor Recovery

arXiv: https://arxiv.org/abs/2311.00783 · HTML: https://mlsanity.com/paper/2311.00783/

## Key facts

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

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

- [Power of ℓ1-Norm Regularized Kaczmarz Algorithms for High-Order Tensor Recovery](https://mlsanity.com/paper/2405.08275/) (2024)

## Abstract (arXiv)

Sparse and low rank tensor recovery has emerged as a significant area of research with applications in many fields such as computer vision. However, minimizing the ℓ0-norm of a vector or the rank of a matrix is NP-hard. Instead, their convex relaxed versions are typically adopted in practice due to the computational efficiency, e.g., log-sum penalty. In this work, we propose novel log-sum regularized Kaczmarz algorithms for recovering high-order tensors with either sparse or low-rank structures. We present block variants along with convergence analysis of the proposed algorithms. Numerical experiments on synthetic and real-world data sets demonstrate the effectiveness of the proposed methods.