Work

Low-rank tensor completion with fractal-inspired multi-scale energy regularization

Year: 2026

Type: article

Abstract: Low-rank tensor completion has become a fundamental tool for recovering high-dimensional data from incomplete observations. However, conventional methods rely primarily on algebraic low-rank priors and do not explicitly regulate how signal energy is distributed across scales. This study introduces a fractal-inspired multi-scale energy regularization that enforces approximate power-law scaling of tensor energy across resolution levels. The proposed formulation integrates scale-consistency constraints with tensor nuclear norm regularization in a unified framework. An inexact ADMM algorithm is developed to solve the resulting non-convex problem. Experimental results demonstrate consistent improvements in reconstruction accuracy across tensor sizes and observation ratios.

Source: Frontiers in Applied Mathematics and Statistics

DOI: 10.3389/fams.2026.1809903

Authors: Chuling Wen, Weijie Liang, Chen Xu, Yuru Zou

Institution: Shenzhen University

Language: English

Topic: Tensor decomposition and applications

Subfield: Computational Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,418

Funders: National Natural Science Foundation of China, Natural Science Foundation of Guangdong Province