A tomographic reconstruction technique of a 3D internal distribution of defects, from an incomplete and noisy data set, is presented. The associated direct problem is solved numerically by the finite analytic method, using an alternating direction implicit approach. A constrained optimisation algorithm together with a maximum entropy regularisation technique is used to solve the inverse problem. Numerical results, obtained from data sets simulated by the direct model and corrupted by Gaussian noise, demonstrate the good general performance of the proposed inversion method.