Tensor robust principal component analysis with total generalized variation for high-dimensional data recovery

Zhi Xu, Jing-Hua Yang, Chuan-long Wang, Fusheng Wang and Xi-hong Yan

Applied Mathematics and Computation, 2024, vol. 483, issue C

Abstract: In the past few years, tensor robust principal component analysis (TRPCA) which is based on tensor singular value decomposition (t-SVD) has got a lot of attention in recovering low-rank tensor corrupted by sparse noise. However, most TRPCA methods only consider the global structure of the image, ignoring the local details and sharp edge information of the image, resulting in the unsatisfactory restoration results. In this paper, to fully preserve the local details and edge information of the image, we propose a new TRPCA method by introducing a total generalized variation (TGV) regularization. The proposed method can simultaneously explore the global and local prior information of high-dimensional data. Specifically, the tensor nuclear norm (TNN) is employed to develop the global structure feature. Moreover, we introduce the TGV, a higher-order generalization of total variation (TV), to preserve the local details and edges of the underlying image. Subsequently, the alternating direction method of multiplier (ADMM) algorithm is introduced to solve the proposed model. Sufficient experiments on color images and videos have demonstrated that our method is superior to other comparison methods.

Keywords: Tensor robust principal component analysis; Total generalized variation; Tensor singular value decomposition; Tensor nuclear norm; The alternating direction method of multiplier algorithm (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:483:y:2024:i:c:s0096300324004417

DOI: 10.1016/j.amc.2024.128980

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