We consider in this paper the problem of reconstructing 3D Computed Tomography images from limited data. The problem is modeled as a nonnegatively constrained minimization problem of very large size. In order to obtain an acceptable image in short time, we propose a scaled gradient projection method, accelerated by exploiting a suitable scaling matrix and efficient rules for the choice of the step-length. In particular, we select the step-length either by alternating Barzilai-Borwein rules or by exploiting a limited number of back gradients for approximating second-order information. Numerical results on a 3D Shepp-Logan phantom are presented and discussed.
A fast gradient projection method for 3D image reconstruction from limited tomographic data
LOLI PICCOLOMINI, ELENA;MOROTTI, ELENA;
2017
Abstract
We consider in this paper the problem of reconstructing 3D Computed Tomography images from limited data. The problem is modeled as a nonnegatively constrained minimization problem of very large size. In order to obtain an acceptable image in short time, we propose a scaled gradient projection method, accelerated by exploiting a suitable scaling matrix and efficient rules for the choice of the step-length. In particular, we select the step-length either by alternating Barzilai-Borwein rules or by exploiting a limited number of back gradients for approximating second-order information. Numerical results on a 3D Shepp-Logan phantom are presented and discussed.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.