鲁棒张量主成分分析的非凸框架

The Nonconvex Framework for Robust Tensor Principal Component Analysis

非凸鲁棒张量主成分分析问题包括从被噪声破坏的张量中恢复低秩和稀疏部分,这在广泛的实际应用中引起了极大的关注。然而,现有的非凸方法面临许多问题,其中最重要的两个问题是对特定非凸函数的限制和低秩部分的信息损失。在本文,我们提出了一种广义非凸鲁棒张量主成分分析模型(N-RTPCA),其中包括一些最常用的非凸函数。并且提出了一个非凸ADMM算法来求解广义非凸鲁棒张量主成分分析模型(N-RTPCA)。最后,实验部分通过模拟实验和真实图片的实验验证了所提方法的优越性。

The problem of nonconvex robust tensor principal component analysis,which consists of recovering the low-rank part and sparse part of a tensor corrupted by noise,has attracted great atten-tion in a wide range of practical applications.However,existing nonconvex methods face many problems,the two most important of which are the restriction to specific nonconvex functions and the loss of information in the low-rank part.In this paper,we propose a generalized nonconvex robust tensor principal component analysis model(N-RTPCA)which includes some of the most commonly used nonconvex functions.And a nonconvex ADMM algorithm is proposed to solve the generalized nonconvex robust tensor principal component analysis model(N-RTPCA).Finally,the experimental part verifies the superiority of the proposed method by simulation experiments and experiments on real pictures.