Nonlinear least square estimation of geometrical parameters for cone-beam three dimensional computed tomography

The accuracy of reconstructing geometrical parameters is precisely controlled in three-dimensional computed tomography. Because in practical X-ray imaging system, they can not be measured through direct methods, how to ensure their accuracy becomes the spiny problem. The nonlinear least square estimation of three-dimensional reconstructing geometrical parameters based on Feldkamp-type algorithm is introduced. According to the rule that the projection address of a particle in imaging space is as the same as the centroids of its projection. The parameter optimal value is estimated through calculating centroids of the measured projections of a point source (or an object close to a point source) and solving nonlinear equation sets. Computer simulation proves that when the initial value of the parameters are close to their true value, the estimating results are satisfactory and of good repetition. In addition, the parameter optimal value of the practical testing system estimated by this method is applied to image reconstruction, and the satisfying results are also obtained.