Computation and stability analysis for regularized tomographic reconstructions

Deals mainly with the assessment of the stability of various reconstruction methods for computed tomography. The authors also present the convex dual formulation of the optimization problems in entropy-like methods. For each of these methods, the influence of errors in the measured data on the reconstructed image is analyzed. A small perturbation of the data vector induces a perturbation of the reconstructed image which can be computed by means of the sensitivity matrix. Using appropriate matrix computation techniques, an upper bound on the size of the reconstruction error is determined, as well as the pattern of noise in the sinogram that will result in the largest reconstruction error and the standard deviation map in the reconstructed image domain. Simulations illustrate the authors´ analysis and demonstrate its utility in the interpretation of computed images and in the selection of reconstruction parameters.