Joint Gaussian dictionary learning and tomographic reconstruction. (1st October 2022)

• Record Type: Journal Article
• Authors: Zickert, Gustav; Öktem, Ozan; Yarman, Can Evren
• Is Part Of: Inverse problems. Volume 38:Number 10(2022)
• Publication Date: 2022-10-01
• Subjects: dictionary learning -- inverse problem -- tomography -- task adapted reconstruction -- image reconstruction -- sparse coding -- regularization; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ac8bee
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: 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.