Forward model with space-variant of source size for reconstruction on   x-ray radiographic image
  Forward imaging technique is the base of combined method on density reconstruction with the forward calculation and inverse problem solution. In the paper, we introduced the projection equation for the radiographic system with areal source blur and detector blur, gained the projecting matrix from any point source to any detector pixel with x-ray trace technique, proposed the ideal on gridding the areal source as many point sources with different weights, and used the blurring window as the effect of the detector blur. We used the forward projection equation to gain the same deviation information about the object edge as the experimental image. Our forward projection equation is combined with Constrained Conjugate Gradient method to form a new method for density reconstruction, XTRACE-CCG. The new method worked on the simulated image of French Test Object and experimental image. The same results have been concluded the affecting range of the blur is decreased and can be controlled to one or two pixels. The method is also suitable for reconstruction of density-variant object. The capability of our method to handle blur effect is useful for all radiographic systems with larger source size comparing to pixel size. 
Jin Liu, Jun Liu, Yue-feng Jing, Bo Xiao, Cai-hua Wei, Yong-hong Guan,   Xuan Zhang
physics.med-ph physics.data-an