Reduce does exposure in computed tomography (CT) scan has been received much attention in recent years. It is
reasonable to reduce the number of projections for reducing does. However, conventional CT image reconstruction
methods will lead to streaking artifact due to few-view data. Inspired by the theory of compressive sensing, the
total variation minimization method was widely studied in the CT image reconstruction from few-view and
limited-angle data. It takes full advantage of the sparsity in the image gradient magnitude. In this paper, we
propose a general prior image constrained compressed sensing model and develop an efficient iterative algorithm
to solve it. The main idea of our approach is to reformulate the optimization problem as an unconstrained
optimization problem with the sum of two convex functions. Then we derive the iterative algorithm by use of
the primal dual proximity method. The prior image is reconstructed by a conventional analytic algorithm such
as filtered backprojection (FBP) or from a dynamic CT image sequences. We demonstrate the performance of
the proposed iterative algorithm in a quite few-view projection data with just 3 percent of the reconstructed
image size. The numerical simulation results show that the proposed reconstruction algorithm outperforms the
commonly used total variation minimization method.
Computed tomography (CT) image reconstruction problems can be solved by finding the minimization of a suitable objective function. The first-order methods for image reconstruction in CT have been popularized in recent years. These methods are interesting because they need only the first derivative information of the objective function and can solve non-smooth regularization functions. In this paper, we consider a constrained optimization problem which often appeared in the CT image reconstruction problems. For the unconstrained case, it has been studied recently. We dedicate to propose an efficient algorithm to solve the constrained optimization problem. Numerical experiments to image reconstruction benchmark problem show that the proposed algorithms can produce better reconstructed images in signal-to-noise than the original algorithm and other state-of-the-art methods.