Robust principal component analysis (RPCA) is a technique that aims to make principal component analysis (PCA) robust to noise samples. The current modeling approaches of RPCA were proposed by analyzing the prior distribution of the reconstruction error terms. However, these methods ignore the influence of samples with large reconstruction errors, as well as the valid information of these samples in principal component space, which will degrade the ability of PCA to extract the principal component of data. In order to solve this problem, Fuzzy sparse deviation regularized robust principal component Analysis (FSD-PCA) is proposed in this paper. First, FSD-PCA learns the principal components by minimizing the square of $\ell _{2}$ -norm-based reconstruction error. Then, FSD-PCA introduces sparse deviation on reconstruction error term to relax the samples with large bias, thus FSD-PCA can process noise and principal components of samples separately as well as improve the ability of FSD-PCA for retaining the principal component information. Finally, FSD-PCA estimates the prior probability of each sample by fuzzy weighting based on the relaxed reconstruction error, which can improve the robustness of the model. The experimental results indicate that the proposed model performs excellent robustness against different types of noise than the state-of-art algorithms, and the sparse deviation term enables FSD-PCA to process noise information and principal component information separately, so FSD-PCA can filter the noise information of an image and restore the corrupted image.

中文翻译：

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模糊稀疏偏差正则化稳健主成分分析

稳健主成分分析 (RPCA) 是一种旨在使主成分分析 (PCA) 对噪声样本具有稳健性的技术。通过分析重构误差项的先验分布，提出了当前的RPCA建模方法。然而，这些方法忽略了重构误差较大的样本的影响，以及这些样本在主成分空间中的有效信息，这会降低PCA提取数据主成分的能力。为了解决这个问题，本文提出了模糊稀疏偏差正则化鲁棒主成分分析法（FSD-PCA）。首先，FSD-PCA 通过最小化平方来学习主成分 $\ell _{2}$ -基于范数的重建错误。然后，FSD-PCA在重构误差项上引入稀疏偏差以放松具有大偏差的样本，从而FSD-PCA可以分别处理样本的噪声和主成分，提高FSD-PCA保留主成分信息的能力。最后，FSD-PCA基于松弛的重构误差通过模糊加权估计每个样本的先验概率，可以提高模型的鲁棒性。实验结果表明，该模型对不同类型噪声的鲁棒性优于现有算法，稀疏偏差项使 FSD-PCA 能够分别处理噪声信息和主成分信息，因此 FSD-PCA 可以过滤图像的噪声信息并恢复损坏的图像。