Principal component analysis based on block-norm minimization

Principal Component Analysis (PCA) has attracted considerable interest for years in the studies of image recognition. So far, several state-of-the-art PCA-based robust feature extraction techniques have been proposed, such as PCA-L1 and R1-PCA. Since those methods treat image by its transferred vector form, it leads to the loss of latent information carried by images and loses sight of the spatial structural details of image. To exploit these two kinds of information and improve robustness to outliers, we propose principal component analysis based on block-norm minimization (Block-PCA) which employs block-norm to measure the distance between an image and its reconstruction. Block-norm imposes L2-norm constrain on a local group of pixel blocks and uses L1-norm constrain among different groups. In the case where parts of an image are corrupted, Block-PCA can effectively depress the effect of corrupted blocks and make full use of the rest. In addition, we propose an alternative iterative algorithm to solve the Block-PCA model. Performance is evaluated on several datasets and the results are compared with those of other PCA-based methods.