Abstract: Different convolution kernels can obtain different image features, but training convolution kernels is difficult. To tackle this problem, an image classification algorithm based on the Principal Component Analysis （PCA） convolution and sparse representation is proposed. First, training samples are divided into small slices with mean-removed, then the PCA algorithm is directly applied to extract the first K eigenvectors as convolution kernels, then convolution operation is carried out for the original image and an automatic weighting strategy is proposed for integrating the image features obtained by convolution processing. Lastly, histogram statistics is used and the sparse representation algorithm is exploited for classification. Extensive experiments on representative face databases including AR, CMU Multi-PIE, ORL and digital handwriting dataset MNIST demonstrate that the proposed algorithm can get better recognition than state-of-the-art methods.

Key words: sparse representation, Principal Component Analysis（PCA） convolution kernel, image convolution, histogram, image classification

摘要： 针对不同卷积核可以提取不同的图像特征，而卷积核的训练比较困难这一问题，提出一种带主成分分析（PCA）卷积的稀疏表示分类算法。先对训练样本集做分片去均值化处理，然后直接应用PCA算法提取所有分片的前K个特征向量作为卷积核，再用这些卷积核对原始图像进行卷积操作；并提出一种自动加权策略，对卷积处理后得到的K个特征图像进行加权叠加操作；最后对特征图像进行分块直方图统计稀疏化，并应用稀疏表示分类算法进行分类。在公共人脸数据集AR、CMU Multi-PIE、ORL以及数字手写体数据集MNIST上与常用分类算法进行对比实验，实验结果表明，带PCA卷积的稀疏表示分类算法具有更高的分类准确率。

关键词: 稀疏表示, 主成分分析卷积核, 图像卷积, 直方图统计, 图像分类