References & Citations
Mathematics > Optimization and Control
Title: Log-Sum Regularized Kaczmarz Algorithms for High-Order Tensor Recovery
(Submitted on 1 Nov 2023 (v1), last revised 19 Apr 2024 (this version, v2))
Abstract: 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 $\ell_0$-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.
Submission history
From: Jing Qin [view email][v1] Wed, 1 Nov 2023 19:02:15 GMT (629kb,D)
[v2] Fri, 19 Apr 2024 21:00:26 GMT (614kb,D)
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