Information divergence constrained total variation minimization for positron emission tomography image reconstruction

To achieve high-definition positron emission tomography (PET) reconstruction, this paper presents an α-divergence constrained total variation (αD-TV) minimization approach based on information divergence measure. In the cost function construction, we use α-divergence to measure the discrepancy between the measured and estimated data; and utilize total variation as a regularization to regularize the solution. For solving the cost function, an αD-TV algorithm is developed. Specially, for optimizing the cost function, a semi-implicit iteration scheme is utilized firstly according to the subgradient theory. Then, the semi-implicit iteration scheme is realized by alternating the α-divergence minimization and image TV minimization. In order to guarantee the convergence of the presented αD-TV algorithm, an adaptive nonmonotone line search scheme is further adopted. The experimental results from the simulated and real data demonstrate that the presented αD-TV algorithm performs better than other conventional methods in suppressing the noise and preserving the edge detail.