Joint Gaussian dictionary learning and tomographic reconstruction

作     者：Zickert, Gustav Oktem, Ozan Yarman, Can Evren 

作者机构：KTH Royal Inst Technol Dept Math SE-10044 Stockholm Sweden Etud & Prod Schlumberger 1 Rue Henri Becquerel F-92140 Clamart France 

出 版 物：《INVERSE PROBLEMS》 (逆问题)

年 卷 期：2022年第38卷第10期

页      面：105010-105010页

核心收录：

学科分类：07[理学] 0701[理学-数学] 0702[理学-物理学] 

基　　金：Swedish Foundation of Strategic Research [AM13-0049] Swedish Foundation for Strategic Research (SSF) [AM13-0049] Funding Source: Swedish Foundation for Strategic Research (SSF) 

主　　题：dictionary learning inverse problem tomography task adapted reconstruction image reconstruction sparse coding regularization 

摘      要：This paper studies ill-posed tomographic imaging problems where the image is sparsely represented by a non-negative linear combination of Gaussians. Our main contribution is to develop a scheme for directly recovering the Gaussian mixture representation of an image from tomographic data, which here is modeled as noisy samples of the parallel-beam ray transform. An important aspect of this non-convex reconstruction problem is the choice of initial guess. We propose an initialization procedure that is based on a filtered back projection type of operator tailored for the Gaussian dictionary. This operator can be evaluated efficiently using an approximation of the Riesz-potential of an anisotropic Gaussian which is based on an exact closed form expression for the Riesz-potential of an isotropic Gaussian. The proposed method is evaluated on simulated data.