Particle Swarm Optimization Of Fuzzy Penalty For 3D Image Reconstruction In X-Ray Tomography A.M.T.Gouicem 1 , M.Yahi 1 , A.Taleb-Ahmed 2 , R.Drai 1 1 Laboratory of Image and Signal Processing (LISP) CSC Research Centre in Welding and NDT Algiers, Algeria medthrali@yahoo.fr 2 LAMIH UMR CNRS UVHC 8201, Valenciennes, France Abstract Engineers last year's works only on the 2D image data, to perceive defects in the CT images. This was a handicap facing the challenge of determining the 3D exact defect form. This paper presents a method for 3D image reconstruction, the most interesting in non destructive testing (NDT) especially due to its application in industrial imaging. We propose a new combined approach using particle swarm optimization (PSO) and fuzzy inference penalty, which will be helpful to elevate the hard inverse problem of 3D computed tomography. Introduction Image reconstruction in 3D x-ray tomography consists in determining an object f(x,y,z) from its projections p[1] .A 2-D image represents the projection of a 3-D scene onto a plane, The procedure for detecting edges in 3-D closely follows that in 2-D. But edge contours in 2-D become edge surfaces in 3-D. To avoid detection of noisy edges, it is important that the image is smoothed with a Gaussian before carrying out functional approximation. f(i,j) is the central voxel value and others are 26 neighbors voxel value in 3*3*3 windows. Figure 1: 3D Image representation.