title: Multivariate compressive sensing for image reconstruction in the wavelet domain: using scale mixture models.
abstract: Most wavelet-based reconstruction methods of compressive sensing (CS) are developed under the independence assumption of the wavelet coefficients. However, the wavelet coefficients of images have significant statistical dependencies. Lots of multivariate prior models for the wavelet coefficients of images have been proposed and successfully applied to the image estimation problems. In this paper, the statistical structures of the wavelet coefficients are considered for CS reconstruction of images that are sparse or compressive in wavelet domain. A multivariate pursuit algorithm (MPA) based on the multivariate models is developed. Several multivariate scale mixture models are used as the prior distributions of MPA. Our method reconstructs the images by means of modeling the statistical dependencies of the wavelet coefficients in a neighborhood. The proposed algorithm based on these scale mixture models provides superior performance compared with many state-of-the-art compressive sensing reconstruction algorithms.
authors.affiliation: School of Computer Science and Technology, Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education of China, Xidian University, Xi’an 710071, China. wu_jiao@yahoo.cn
authors.forename: Jiao
authors.initials: J
authors.lastname: Wu
authors.forename: Fang
authors.initials: F
authors.lastname: Liu
authors.forename: L C
authors.initials: LC
authors.lastname: Jiao
authors.forename: Xiaodong
authors.initials: X
authors.lastname: Wang
authors.forename: Biao
authors.initials: B
authors.lastname: Hou