增强的张量鲁棒主成分分析模型及其应用

鲁棒主成分分析（RPCA）是处理图像恢复和背景建模问题的常用模型。针对原始RPCA及其改进模型对输入数据低秩结构的依赖性过强问题，提出一个增强的张量鲁棒主成分分析模型（E-TRPCA）并构造了一个新的增强张量核范数（E-TNN）正则项。E-TNN基于张量数据的低维子空间投影约束其低秩性，可以更真实地反映张量数据的潜在结构，增强模型的泛化性。利用交替方向乘子算法（ADMM）对目标函数进行优化求解，在图像去噪和背景建模上的实验结果表明所提方法在图像恢复效果和运行时间方面要优于当前的其他方法。

Applications of enhanced tensor robust principal component analysis

Robust principal component analysis(RPCA) is a popular model to deal with image restoration and background modeling problems. By focusing on the problem of the excessive dependence of the original RPCA and an improved model based on the low-rank structure of the input data, we propose an enhanced robust principal component analysis model and design a new enhanced tensor nuclear norm. To naturally reflect the intrinsic structure of the tensor and improve the generalization of the model, E-TNN restricts the low-rank properties of the tensor data via its low dimensional subspace bases. The augmented Lagrange multiplier method is used to optimize the objective function. Experimental measurements of image denoising and background modeling show that the proposed method outperforms other current methods in terms of image restoration effect and running time.