Affiliations: Imaging and Medical Physics, Department of Radiology
and Imaging Sciences, Emory University School of Medicine, Atlanta, GA,
USA | School of Automation, Xi'an University of Posts and
Telecommunications, Xi'an, Shaanxi, China
Note: [] Corresponding author: Xiangyang Tang, Ph.D., Imaging and Medical
Physics, Department of Radiology and Imaging Sciences, Emory University School
of Medicine, 1701 Uppergate Dr., C5018, Atlanta, GA 30322, USA. Tel.: +1 404
778 1732; Fax: +1 404 712 5813; E-mail: xiangyang.tang@emory.edu
Abstract: Purposes: Interior tomography problem can be solved using the
so-called differentiated backprojection-projection onto convex sets (DBP-POCS)
method, which requires a priori knowledge within a small area interior
to the region of interest (ROI) to be imaged. In theory, the small area wherein
the a priori knowledge is required can be in any shape, but most of
the existing implementations carry out the Hilbert filtering either
horizontally or vertically, leading to a vertical or horizontal strip that may
be across a large area in the object. In this work, we implement a practical
DBP-POCS method with radial Hilbert filtering and thus the small area with the
a priori knowledge can be roughly round (e.g., a sinus or ventricles
among other anatomic cavities in human or animal body). We also conduct an
experimental evaluation to verify the performance of this practical
implementation. Methods: We specifically re-derive the reconstruction
formula in the DBP-POCS fashion with radial Hilbert filtering to assure that
only a small round area with the a priori knowledge be needed (namely
radial DBP-POCS method henceforth). The performance of the practical DBP-POCS
method with radial Hilbert filtering and a priori knowledge in a small
round area is evaluated with projection data of the standard and modified
Shepp-Logan phantoms simulated by computer, followed by a verification using
real projection data acquired by a computed tomography (CT) scanner. Results: The preliminary performance study shows that, if a
priori knowledge in a small round area is available, the radial DBP-POCS
method can solve the interior tomography problem in a more practical way at
high accuracy. Conclusions: In comparison to the implementations of
DBP-POCS method demanding the a priori knowledge in horizontal or
vertical strip, the radial DBP-POCS method requires the a priori
knowledge within a small round area only. Such a relaxed requirement on the
availability of a priori knowledge can be readily met in practice,
because a variety of small round areas (e.g., air-filled sinuses or
fluid-filled ventricles among other anatomic cavities) exist in human or animal
body. Therefore, the radial DBP-POCS method with a priori knowledge in
a small round area is more feasible in clinical and preclinical practice.
