Polynomial accelerated algorithm base on minimizing TV for computerized tomographic image reconstruction

Based on total variation minimization (TV) algorithm and the theory of polynomial acceleration, we prompted a modified algorithm, which is called P-TV in this paper. This new algorithm has a better noise immunity and fewer iteration numbers than the traditional TV algorithm. P-TV algorithm can be divided into four steps. Compared to the traditional TV algorithm, the P-TV algorithm applies the theory of polynomials to ART iteration step to enforce data consistency with the projection data and applies the positivity constraint after the GRAD-step too, which accelerate convergence of image reconstruction. Simulation results prove that when the iteration number is the same, the quality of reconstructed image from P-TV algorithm is better than traditional TV algorithm. When the quality of image reconstructed by both algorithms is nearly the same, the iteration number of P-TV algorithm is much less than the number of traditional TV algorithm. At last we applied the two algorithms to CT image reconstruction from the noisy data. All results show that the P-TV algorithm is effective.