To achieve high diagnostic PET imaging

we propose a novel total variation (TV) based alpha-divergence minimization reconstruction algorithm.The presented cost function uses the alpha-divergence to measure the discrepancy between the measured and the estimated emission projection data and utilizes the TV regularization to regularize the consistency of solution.A semi-implicit iteration scheme is used in the proposed algorithm by adapting the subgradient theory; and then an adaptive nonmonotone line search scheme is taken to guarantee the algorithm convergence.The experiments from the simulated phantom data and the real emission data show that the presented algorithm performs better than the other classical PET reconstruction methods in the noise suppressing and the edge details preserving.