4.6 Article

Joint Gaussian dictionary learning and tomographic reconstruction

期刊

INVERSE PROBLEMS
卷 38, 期 10, 页码 -

出版社

IOP Publishing Ltd
DOI: 10.1088/1361-6420/ac8bee

关键词

dictionary learning; inverse problem; tomography; task adapted reconstruction; image reconstruction; sparse coding; regularization

资金

  1. Swedish Foundation of Strategic Research [AM13-0049]
  2. Swedish Foundation for Strategic Research (SSF) [AM13-0049] Funding Source: Swedish Foundation for Strategic Research (SSF)

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This paper proposes a method for recovering images from ill-posed tomographic imaging problems using a Gaussian mixture representation. The study focuses on the choice of initial guess and proposes an initialization procedure based on a filtered back projection operator tailored for the Gaussian dictionary. The proposed method is evaluated using simulated data.
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.

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