Robust tensor completion improves multidimensional data recovery quality
Robust low-rank tensor completion via factorized weighted tensor schatten-p norm minimization
Computer Vision and Pattern Recognition
Summary
Filling in missing or damaged parts of complex data that has multiple dimensions, like color images or 3D scans, is challenging because standard techniques can weaken important information. The authors created new mathematical tools that handle different parts of the data more carefully and efficiently, avoiding costly computations. These tools help better restore incomplete or corrupted multidimensional data by focusing on the strongest components while removing less important ones. Their experiments show that these methods outperform existing ones on several tasks involving images and sensor data.
What this means in practice
- •For image processing engineers: Enhance image restoration tasks including color and hyperspectral image inpainting with improved accuracy from robust tensor completion models.
- •For electronics quality control teams: Detect defects on printed circuit boards more reliably using robust completion of incomplete sensor or image data.
Authors
Binghao Wang, Feng Zhang, Wendong Wang, Jianjun Wang
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-$δ$ 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.