Research
Robust low-rank tensor completion via factorized weighted tensor schatten-p norm minimization
arXiv:2609.14307v1 Announce Type: new Abstract: Low-rank tensor factorization provides a flexible framework for completing multidimensional data from incomplete and corrupted observations. However, un
arXiv:2609.14307v1 Announce Type: new Abstract: Low-rank tensor factorization provides a flexible framework for completing multidimensional data from incomplete and corrupted observations. However, unweighted spectral regularizers impose a common shrinkage profile across singular components, which may excessively attenuate dominant low-rank components, and factorized variants either lack component-specific weighting or require costly singular value decompositions (SVDs). This paper proposes two weighted Schatten-p tensor factorization models, termed WSpTFI{} and WSpTFII{}, under the tensor-tensor product (t-product) framework to address these limitations. WSpTFI{} is motivated by a factorized weighted tensor Schatten-p norm identity and permits flexible, possibly asymmetric factor exponents. WSpTFII{} constructs a regularizer from transform-domain column-pair energies, yielding SVD-free main factor updates and a column-pruning mechanism for reducing redundant rank components. This paper further develops an iteratively reweighted alternating direction method of multipliers (ADMM)-type scheme for WSpTFI{} and an iteratively reweighted least squares (IRLS)--block successive upper-bound minimization (BSUM) scheme for WSpTFII{}. Theoretical analysis establishes the weighted factorization relation and provides a conditional limiting Karush--Kuhn--Tucker (KKT) characterization for WSpTFI{}. For WSpTFII{}, the actual damped quadratic block updates yield a quantitative sufficient-decrease mechanism for the fixed-elta smoothed factor objective. This implies asymptotic regularity, and every accumulation point of the fixed-dimensional tail is stationary. Experiments on synthetic tensor completion, color-image restoration, hyperspectral inpainting, and printed-circuit-board defect detection demonstrate competitive reconstruction quality and robustness under various degradation conditions.
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Source: arXiv cs.CV | 2026-09-15