图像矩阵上的广义最大噪声分离算法

主成分分析（PCA）是模式识别中一种重要的变换工具，在图像处理的特征提取和降维方面有广泛的应用。然而，由于二维图像数据需要进行向量化处理，导致高维向量的产生和像素空间位置丢失。广义主成分分析（GPCA）则是基于图像矩阵的主成分分析推广算法，它不改变像素间的空间位置关系，而且计算量也显著降低。但主成分分析和广义主成分分析都没有考虑到实际图像中存在的噪声干扰。最大噪声分离（MNF）则是一种面向噪声干扰的变换方法，与主成分分析基于方差的最大化不同，最大噪声分离是基于信噪比的最大化。与GPCA的推广类似，在图像二维矩阵上推广最大噪声分离方法，提出一种广义最大噪声分离（GMNF）算法。该变换方法在保证重构时信噪比最大的同时，也具有不改变像素空间位置、计算量小的优点。在人脸和红外图像上的仿真实验结果验证了所提算法的有效性。

Generalized maximum noise fraction on image matrix

Principal Component Analysis (PCA) is an important transform method in pattern recognition and is widely used in feature extraction and dimensionality reduction. However, since the two-dimensional images must be converted into one-dimensional vectors, there will be high dimensional data and the spatial information of pixels will be lost. Generalized Principal Component Analysis (GPCA) is the extension of PCA on two-dimensional image matrix, which does not change the location information of pixels, and its calculation cost is also significantly reduced. However, neither PCA or GPCA considers the noise that unavoidably exists in actual images. Maximum Noise Fraction (MNF) is a transform method that is designed to decrease noise. In contrast to the maximization of variance for PCA, MNF is based on the maximization of Signal-Noise Ratio (SNR). Similar to GPCA, this paper extends MNF on two-dimensional image matrix and proposes a Generalized Maximum Noise Fraction (GMNF) algorithm. GMNF is also based on the maximization of SNR. Meanwhile, GMNF does not lose the spatial information of pixels and has less computational complexity. Experimental results on face and hyperspectral images verify the effectiveness of the proposed algorithm.