Joint Gaussian dictionary learning and tomographic reconstruction

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 a procedure for initializations 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.

Low-resolution prior equilibrium network for CT reconstruction

“…In general, when the number of pixels in a reconstructed image exceeds the number of projection samples in CT imaging, the inverse problem of (1) becomes ill-posed. Due to the radiation, various approaches have been explored, which can be primarily categorized into two main categories, either to modify the scanning protocol by reducing the tube voltage and/or tube current [44] or downsample the measured data for CT reconstruction, such as interior CT [36,51,60,70], and sparse-view CT [34,63,65,66,68,72]. These approaches aim to achieve dose reduction while maintaining satisfactory image quality.…”