Abstract: In this paper, we study a constrained separable convex optimization model, in which the data error term in the objective function is differentiable. Many problems arising in image restoration and image reconstruction are the special cases of this convex optimization problem. In order to overcome the shortcomings of existing methods for solving this model, we transform the original problem into an unconstrained convex optimization problem by using an indicator function. Then, we propose a new iterative algorithm, which is based on the idea of the primal-dual splitting method. The proposed algorithm has a simple structure and is easy for parameter selection. At the same time, we prove the convergence of the new iterative algorithm. Finally, to verify its effectiveness, we apply the algorithm to CT image reconstruction. Numerical experiments show that the proposed algorithm outperforms existing iterative algorithms in terms of reconstruction time and reconstruction image quality.

Key words: separable convex programs, primal-dual splitting method, image reconstruction, proximity operator