Compressive representation based pattern analysis for correlation image

Abstract

The definition of the correlation image for digital image is presented to show that the correlation images of different images exhibit distinct texture-like appearances. Then inspired by the universality of the compressive sensing theory which indicates that random measurements can be employed for signals sparse in any basis, the compressive representation for digital image is further defined by employing random matrix as sensing matrix to measure the correlation image. It is found that l vectors of the compressive representation for one image exhibit a highly coherent similarity while display distinct characteristics between different images as well. Thus it shows that one image can be well compressively represented by using one of the l vectors as the feature vector of compressive representation in the sensing (measurement) domain. As data dimension of the feature vector is much less than that of both the original image and the correlation image, it facilitates pattern analysis for its less computational complexity. Application results of face recognition indicate potentiality of the proposed method. Further performance analysis based on tests of the leave-one-out cross-validation, twofold cross-validation as well as analysis of variance shows that the proposed method outperforms the classical PCA on the face recognition tasks.