Compressive representation based pattern analysis for correlation image
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ORIGINAL ARTICLE
Compressive representation based pattern analysis for correlation image Zong-chang Yang1
Received: 3 May 2015 / Accepted: 5 February 2016 Springer-Verlag Berlin Heidelberg 2016
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. Keywords Correlation image Random sensing Compressive representation Pattern analysis
& Zong-chang Yang [email protected] 1
School of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan 411201, China
1 Introduction Texture may be easily recognized by people when people see it. However, no precise definition of the notion texture is provided but many from a certain perspective, such as a definition [1] of a function of the spatial variation in pixel intensities (gray values). While image texture is useful in a variety of applications [2–4], such as image segmentation or classification of images, etc. Recently, an emerging technique called the compressive sensing (also called the compressed sensing or sparse sampling) [5–12] has become a subject of intense study. It seems to have a broad application prospect for its potential advantages: (1) nonadaptive sampling which breaks through the limitation of Shannon sampling theorem. (2) Strong anti-interference ability that every component of the measurement is important or unimportant and then the signal can still be reconstructed with some components being lost. That a signal is supposed to be sparse or compressible is the basic idea behind the compressive sensing. However, few of natural signals are sparse. As indicated by the compressive sensing theory, signal may be sparse by some reversible transforms, such as the wavelet, Fourier, and PCA to find transformations to sparsify the signal. Along
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