摘要： L1-PCA相比传统的主成分分析(PCA)更具鲁棒性，但是L1-PCA算法存在很多局部最优解且秩约束计算较为复杂。为此，提出一种基于迹范数的L1-PCA算法。利用迹范数近似代替矩阵的秩，以解决秩约束存在很多局部最优解的问题，采用基于增强拉格朗日乘子的方法对算法求解，并将其应用于图像的降噪处理。实验结果表明，利用该算法降噪后的图像轮廓清晰、同类图像特征明显趋同。

关键词: 主成分分析, 迹范数, 增强拉格朗日乘子, 闭合形式解, 奇异值分解

Abstract: Compared with Principal Component Analysis(PCA), L1-PCA has better robustness. But, there are some problems in the L1-PCA such as locally optimal solutions, computational complexity of rank. In order to solve the problems, the paper proposes a new algorithm of L1-PCA based on trace norm, it uses trace norm approximate to instead of matrix rank, and solves the problem that rank constraint has many local optimal solution, and the solution algorithm is based on Augmented Lagrange Multiplier(ALM) and applies it in noise reduction of images. Experimental results show that the image outline of this algorithm after doing noise reduction is clear and objects within the same class become more similar.

Key words: Principal Component Analysis(PCA), trace norm, Augmented Lagrange Multiplier(ALM), closed form solution, Singular Value Decomposition(SVD)

中图分类号: 

• TP301.6