Bayesian 3D X-Ray Reconstruction From Incomplete Noisy Data

Abstract

Here the 3D X-Ray Bayesian reconstruction (BR) with Gibbs priors (GP) is considered in the form of quadratic functional (QF) representation of two mechanical and one statistical model being applied to the problem of image restoration from strongly incomplete noisy data. The BR with GP in the form of mechanical modeis as priors can result in an image restoration using 10–100 times less number of projections compared to cone-beam Computer Tomography. The quality of reconstruction as well as the computing time are shown to be strongly dependent upon the form of the a priory model and the noise level. Additionally a new prior is introduced in terms of a statistical model. Results are presented investigating the influence of the applied GP form and the noise level on quality of the reconstruction procedure for which quantitative estimates are provided. Restoration capabilities are compared for three types of models: cluster, plane and phase support algorithm. The influence of the following variables involved in the reconstruction procedure of binary and three level object are investigated: (i) the number of cone-beam projections up to 36, (ii) the level of Gaussian distributed white noise imposed on the 2D projections having the variance up to the value four times larger than the grey level resulted from projecting of one defect voxel, (iii) the form of the prior constraint, (iv) the value of the regularization parameter, and (v) the zero-level approximation before starting the minimization procedure. The error of the reconstruction and the computing time are choosen to be the final estimators of the capability of the method in all cases. Finally, conclusions are drawn about the potential of the method for multi-step BR with GP.