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

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.