PIECEWISE TIKHONOV REGULARIZATION SCHEME TO RECONSTRUCT DISCONTINUOUS DENSITY IN COMPUTERIZED TOMOGRAPHY

In this paper, we proposed a piecewise Tikhonov regularization scheme to overcome the disadvantage of the classical Tikhonov regularization for solving the Radon integral equation whose solution is piecewise continues arising in CT imaging. In our new scheme, we firstly detect the location of discontinuous interface by applying the classical Tikhonov regularization. Then a so-called piecewise Tikhonov regularization method is applied to reconstruction the smooth solution in each piece. Some numerical examples has also be presented to demonstrate the effectiveness of this two-steps scheme.