title: Practical interior tomography with radial Hilbert filtering and a priori knowledge in a small round area.
abstract: OBJECTIVE
  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.
authors: Imaging and Medical Physics, Department of Radiology and Imaging Sciences, Emory University School of Medicine, Atlanta, GA 30322, USA.
authors: Shaojie
authors: S
authors: Tang
authors: Yi
authors: Y
authors: Yang
authors: Xiangyang
authors: X
authors: Tang
mesh_terms: D000465:Algorithms; D000818:Animals; D003198:Computer Simulation; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008962:Models, Theoretical; D019047:Phantoms, Imaging; D012756:Sheep; D014057:Tomography, X-Ray Computed / Q000379:methods*